tag:blogger.com,1999:blog-63054468870533452572024-03-13T10:23:15.842-07:00Compound-Pendulumd8http://www.blogger.com/profile/09390427562617157781noreply@blogger.comBlogger8125tag:blogger.com,1999:blog-6305446887053345257.post-55810938805317110722009-01-12T19:10:00.000-08:002009-01-16T22:03:04.107-08:00Conclusion<p class="MsoNormal" style="line-height:150%;tab-stops:1.0in 81.0pt"><span class="Apple-style-span" style="font-weight: bold;"><br /></span></p> <p class="MsoNormal" style="line-height:150%;tab-stops:1.0in 81.0pt"><b style="mso-bidi-font-weight:normal"><span lang="EN-GB"><o:p> </o:p></span></b></p> <p class="MsoNormal" style="line-height:150%;tab-stops:1.0in 81.0pt"><span lang="EN-GB">Overall, this experiment is not quite a success as there are many factors that influence the error both in readings and apparatus set up. In order to reduce these errors, some consideration has to be taken to improve the experiment, so better performance can be obtained, hence making this experiment a success. In my opinion, the area where the lab is performed should be a closed set so that no blowing winds will affects the pendulum swing. Other than that, the set up for the experiment must be reliable and suitable apparatus must be used to improve the accuracy of readings taken, for example the usage of the ‘allen key’ as the hinge is totally unsuitable. Perhaps, more readings should be taken for each swings and then the average values are calculated, at least the values will not be so much in difference. Lastly, in this matter some errors can be eliminated if some precautions are taken seriously. <span style="mso-spacerun:yes"> </span></span></p> <p class="MsoNormal" style="line-height:150%;tab-stops:1.0in 81.0pt"><span lang="EN-GB"><o:p> </o:p></span></p>d8http://www.blogger.com/profile/09390427562617157781noreply@blogger.com4tag:blogger.com,1999:blog-6305446887053345257.post-64757706861202173382009-01-10T15:01:00.000-08:002009-01-16T22:02:24.133-08:00Discussion<p class="MsoNormal" style="line-height:150%;tab-stops:1.0in 81.0pt"><br /></p> <p class="MsoNormal" style="line-height:150%;tab-stops:1.0in 81.0pt"><b style="mso-bidi-font-weight:normal"><span lang="EN-GB"><o:p> </o:p></span></b></p> <p class="MsoNormal" style="line-height:150%;tab-stops:1.0in 81.0pt"><span lang="EN-GB">From the experiment, I found that there are several differences in between theoretical values and experimental values that being obtained. These differences should not be so obvious. The values supposed to be not much in difference as the experimental and theoretical values should be almost the same. By my inference, there are several factors that influenced these differences. One of the main factors that often occur in any experiment including this experiment is inconsistency while values are taken. Firstly, the hinge where the pendulum is hang is an ‘allen key’ and have 6 surfaces which is not smooth. Thus, the pendulum cannot swing smoothly compared if the hinge used is a smooth circular rod. While the pendulum is released, the angle where the pendulum is released is not accurate. The angle of released are not always the same each time, even the angle supposed to be at <span style="position:relative; top:3.0pt;mso-text-raise:-3.0pt"><!--[if gte vml 1]><v:shapetype id="_x0000_t75" coordsize="21600,21600" spt="75" preferrelative="t" path="m@4@5l@4@11@9@11@9@5xe" filled="f" stroked="f"> <v:stroke joinstyle="miter"> <v:formulas> <v:f eqn="if lineDrawn pixelLineWidth 0"> <v:f eqn="sum @0 1 0"> <v:f eqn="sum 0 0 @1"> <v:f eqn="prod @2 1 2"> <v:f eqn="prod @3 21600 pixelWidth"> <v:f eqn="prod @3 21600 pixelHeight"> <v:f eqn="sum @0 0 1"> <v:f eqn="prod @6 1 2"> <v:f eqn="prod @7 21600 pixelWidth"> <v:f eqn="sum @8 21600 0"> <v:f eqn="prod @7 21600 pixelHeight"> <v:f eqn="sum @10 21600 0"> </v:formulas> <v:path extrusionok="f" gradientshapeok="t" connecttype="rect"> <o:lock ext="edit" aspectratio="t"> </v:shapetype><v:shape id="_x0000_i1025" type="#_x0000_t75" style="'width:18pt;" ole=""> <v:imagedata src="file:///C:\DOCUME~1\d8\LOCALS~1\Temp\msohtml1\01\clip_image001.wmz" title=""> </v:shape><![endif]--><img width="24" height="21" src="file:///C:/DOCUME~1/d8/LOCALS~1/Temp/msohtml1/01/clip_image002.gif" shapes="_x0000_i1025" /></span><!--[if gte mso 9]><xml> <o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1025" drawaspect="Content" objectid="_1293706429"> </o:OLEObject> </xml><![endif]--><span style="mso-spacerun:yes"> </span>since the measurement of the angle is only depended on the protactor which is hold next beside the pendulum. Moreover, the angle is observed with our eyes and at different position. Thus, accuracy in this matter is questionable. Other than that, the time taken for the pendulum swing is also questionable as it is observed also with our eyes. The point where the pendulum starts and ends after ten consecutive swings are not really exact as we cannot really measure when the pendulum change it direction to a reversed swing. The time taken when the pendulum completed ten swin9gs is also not accurate. Even this matter seemed to be unreliable, actually it affects our readings a lot when it comes to calculation. Besides that, the area where this experiment is held is close to the laboratory entrance door and wind is also the factor for the pendulum to swing inconsistently as the wind speed changes all the time. There are times when wind blows quite fast and there are times when no wind blows at all. Thus, all of the factors above do influence the readings taken throughout this experiment and that is why the results vary in some way.</span></p>d8http://www.blogger.com/profile/09390427562617157781noreply@blogger.com8tag:blogger.com,1999:blog-6305446887053345257.post-2910056271713540002009-01-09T22:00:00.000-08:002009-01-16T22:00:58.283-08:00Calculation<p class="MsoNormal" style="line-height:150%"><br /></p> <p class="MsoNormal" style="line-height:150%"><span lang="EN-GB"><o:p> </o:p></span></p> <p class="MsoNormal" style="line-height:150%"><span lang="EN-GB">For compound pendulum B,</span></p> <p class="MsoNormal" style="line-height:150%"><span lang="EN-GB"><o:p> </o:p></span></p> <p class="MsoNormal" style="line-height:150%"><span lang="EN-GB"><span style="position:relative;top:16.0pt;mso-text-raise:-16.0pt"><!--[if gte vml 1]><v:shapetype id="_x0000_t75" coordsize="21600,21600" spt="75" preferrelative="t" path="m@4@5l@4@11@9@11@9@5xe" filled="f" stroked="f"> <v:stroke joinstyle="miter"> <v:formulas> <v:f eqn="if lineDrawn pixelLineWidth 0"> <v:f eqn="sum @0 1 0"> <v:f eqn="sum 0 0 @1"> <v:f eqn="prod @2 1 2"> <v:f eqn="prod @3 21600 pixelWidth"> <v:f eqn="prod @3 21600 pixelHeight"> <v:f eqn="sum @0 0 1"> <v:f eqn="prod @6 1 2"> <v:f eqn="prod @7 21600 pixelWidth"> <v:f eqn="sum @8 21600 0"> <v:f eqn="prod @7 21600 pixelHeight"> <v:f eqn="sum @10 21600 0"> </v:formulas> <v:path extrusionok="f" gradientshapeok="t" connecttype="rect"> <o:lock ext="edit" aspectratio="t"> </v:shapetype><v:shape id="_x0000_i1025" type="#_x0000_t75" style="'width:162.75pt;" ole=""> <v:imagedata src="file:///C:\DOCUME~1\d8\LOCALS~1\Temp\msohtml1\01\clip_image001.wmz" title=""> </v:shape><![endif]--><img width="217" height="53" src="file:///C:/DOCUME~1/d8/LOCALS~1/Temp/msohtml1/01/clip_image002.gif" shapes="_x0000_i1025" /></span><!--[if gte mso 9]><xml> <o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1025" drawaspect="Content" objectid="_1293706319"> </o:OLEObject> </xml><![endif]--></span><span lang="FR" style="mso-ansi-language:FR"><span style="mso-spacerun:yes"> </span><o:p></o:p></span></p> <p class="MsoNormal" style="line-height:150%"><span lang="FR" style="mso-ansi-language: FR"><o:p> </o:p></span></p> <p class="MsoNormal" style="line-height:150%"><span lang="FR" style="mso-ansi-language: FR"><span style="position:relative;top:16.0pt;mso-text-raise:-16.0pt"><!--[if gte vml 1]><v:shape id="_x0000_i1026" type="#_x0000_t75" style="'width:114.75pt;height:39.75pt'" ole=""> <v:imagedata src="file:///C:\DOCUME~1\d8\LOCALS~1\Temp\msohtml1\01\clip_image003.wmz" title=""> </v:shape><![endif]--><img width="153" height="53" src="file:///C:/DOCUME~1/d8/LOCALS~1/Temp/msohtml1/01/clip_image004.gif" shapes="_x0000_i1026" /></span><!--[if gte mso 9]><xml> <o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1026" drawaspect="Content" objectid="_1293706320"> </o:OLEObject> </xml><![endif]--><span style="mso-spacerun:yes"> </span><o:p></o:p></span></p> <p class="MsoNormal" style="line-height:150%"><span lang="FR" style="mso-ansi-language: FR"><span style="position:relative;top:16.0pt;mso-text-raise:-16.0pt"><!--[if gte vml 1]><v:shape id="_x0000_i1027" type="#_x0000_t75" style="'width:105.75pt;height:39pt'" ole=""> <v:imagedata src="file:///C:\DOCUME~1\d8\LOCALS~1\Temp\msohtml1\01\clip_image005.wmz" title=""> </v:shape><![endif]--><img width="141" height="52" src="file:///C:/DOCUME~1/d8/LOCALS~1/Temp/msohtml1/01/clip_image006.gif" shapes="_x0000_i1027" /></span><!--[if gte mso 9]><xml> <o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1027" drawaspect="Content" objectid="_1293706321"> </o:OLEObject> </xml><![endif]--><o:p></o:p></span></p> <p class="MsoNormal" style="line-height:150%;tab-stops:1.0in 81.0pt"><span lang="EN-GB"><span style="position:relative;top:15.0pt;mso-text-raise:-15.0pt"><!--[if gte vml 1]><v:shape id="_x0000_i1028" type="#_x0000_t75" style="'width:90pt;height:36.75pt'" ole=""> <v:imagedata src="file:///C:\DOCUME~1\d8\LOCALS~1\Temp\msohtml1\01\clip_image007.wmz" title=""> </v:shape><![endif]--><img width="120" height="49" src="file:///C:/DOCUME~1/d8/LOCALS~1/Temp/msohtml1/01/clip_image008.gif" shapes="_x0000_i1028" /></span><!--[if gte mso 9]><xml> <o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1028" drawaspect="Content" objectid="_1293706322"> </o:OLEObject> </xml><![endif]--></span></p> <p class="MsoNormal" style="line-height:150%;tab-stops:1.0in 81.0pt"><span lang="EN-GB"><span style="position:relative;top:5.0pt;mso-text-raise:-5.0pt"><!--[if gte vml 1]><v:shape id="_x0000_i1029" type="#_x0000_t75" style="'width:99pt;height:18.75pt'" ole=""> <v:imagedata src="file:///C:\DOCUME~1\d8\LOCALS~1\Temp\msohtml1\01\clip_image009.wmz" title=""> </v:shape><![endif]--><img width="132" height="25" src="file:///C:/DOCUME~1/d8/LOCALS~1/Temp/msohtml1/01/clip_image010.gif" shapes="_x0000_i1029" /></span><!--[if gte mso 9]><xml> <o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1029" drawaspect="Content" objectid="_1293706323"> </o:OLEObject> </xml><![endif]--></span></p> <p class="MsoNormal" style="line-height:150%;tab-stops:1.0in 81.0pt"><span lang="EN-GB"><span style="position:relative;top:7.0pt;mso-text-raise:-7.0pt"><!--[if gte vml 1]><v:shape id="_x0000_i1030" type="#_x0000_t75" style="'width:102.75pt;height:21pt'" ole=""> <v:imagedata src="file:///C:\DOCUME~1\d8\LOCALS~1\Temp\msohtml1\01\clip_image011.wmz" title=""> </v:shape><![endif]--><img width="137" height="28" src="file:///C:/DOCUME~1/d8/LOCALS~1/Temp/msohtml1/01/clip_image012.gif" shapes="_x0000_i1030" /></span><!--[if gte mso 9]><xml> <o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1030" drawaspect="Content" objectid="_1293706324"> </o:OLEObject> </xml><![endif]--><span style="mso-spacerun:yes"> </span>-------- (i)</span></p> <p class="MsoNormal" style="line-height:150%;tab-stops:1.0in 81.0pt"><span lang="EN-GB"><span style="position:relative;top:5.0pt;mso-text-raise:-5.0pt"><!--[if gte vml 1]><v:shape id="_x0000_i1031" type="#_x0000_t75" style="'width:74.25pt;height:17.25pt'" ole=""> <v:imagedata src="file:///C:\DOCUME~1\d8\LOCALS~1\Temp\msohtml1\01\clip_image013.wmz" title=""> </v:shape><![endif]--><img width="99" height="23" src="file:///C:/DOCUME~1/d8/LOCALS~1/Temp/msohtml1/01/clip_image014.gif" shapes="_x0000_i1031" /></span><!--[if gte mso 9]><xml> <o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1031" drawaspect="Content" objectid="_1293706325"> </o:OLEObject> </xml><![endif]--></span></p> <p class="MsoNormal" style="line-height:150%;tab-stops:1.0in 81.0pt"><span lang="EN-GB"><span style="position:relative;top:5.0pt;mso-text-raise:-5.0pt"><!--[if gte vml 1]><v:shape id="_x0000_i1032" type="#_x0000_t75" style="'width:72.75pt;height:17.25pt'" ole=""> <v:imagedata src="file:///C:\DOCUME~1\d8\LOCALS~1\Temp\msohtml1\01\clip_image015.wmz" title=""> </v:shape><![endif]--><img width="97" height="23" src="file:///C:/DOCUME~1/d8/LOCALS~1/Temp/msohtml1/01/clip_image016.gif" shapes="_x0000_i1032" /></span><!--[if gte mso 9]><xml> <o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1032" drawaspect="Content" objectid="_1293706326"> </o:OLEObject> </xml><![endif]--><span style="mso-tab-count:1"> </span><span style="mso-spacerun:yes"> </span>---------- (ii)</span></p> <p class="MsoNormal" style="line-height:150%;tab-stops:1.0in 81.0pt"><span lang="EN-GB">Sub. (ii) into (i)</span></p> <p class="MsoNormal" style="line-height:150%;tab-stops:1.0in 81.0pt"><span lang="EN-GB"><span style="position:relative;top:5.0pt;mso-text-raise:-5.0pt"><!--[if gte vml 1]><v:shape id="_x0000_i1049" type="#_x0000_t75" style="'width:177.75pt;height:18.75pt'" ole=""> <v:imagedata src="file:///C:\DOCUME~1\d8\LOCALS~1\Temp\msohtml1\01\clip_image017.wmz" title=""> </v:shape><![endif]--><img width="237" height="25" src="file:///C:/DOCUME~1/d8/LOCALS~1/Temp/msohtml1/01/clip_image018.gif" shapes="_x0000_i1049" /></span><!--[if gte mso 9]><xml> <o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1049" drawaspect="Content" objectid="_1293706327"> </o:OLEObject> </xml><![endif]--></span></p> <p class="MsoNormal" style="line-height:150%;tab-stops:1.0in 81.0pt"><span lang="EN-GB"><span style="position:relative;top:5.0pt;mso-text-raise:-5.0pt"><!--[if gte vml 1]><v:shape id="_x0000_i1050" type="#_x0000_t75" style="'width:239.25pt;height:18.75pt'" ole=""> <v:imagedata src="file:///C:\DOCUME~1\d8\LOCALS~1\Temp\msohtml1\01\clip_image019.wmz" title=""> </v:shape><![endif]--><img width="319" height="25" src="file:///C:/DOCUME~1/d8/LOCALS~1/Temp/msohtml1/01/clip_image020.gif" shapes="_x0000_i1050" /></span><!--[if gte mso 9]><xml> <o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1050" drawaspect="Content" objectid="_1293706328"> </o:OLEObject> </xml><![endif]--></span></p> <p class="MsoNormal" style="line-height:150%;tab-stops:1.0in 81.0pt"><span lang="EN-GB"><span style="position:relative;top:5.0pt;mso-text-raise:-5.0pt"><!--[if gte vml 1]><v:shape id="_x0000_i1033" type="#_x0000_t75" style="'width:152.25pt;height:18.75pt'" ole=""> <v:imagedata src="file:///C:\DOCUME~1\d8\LOCALS~1\Temp\msohtml1\01\clip_image021.wmz" title=""> </v:shape><![endif]--><img width="203" height="25" src="file:///C:/DOCUME~1/d8/LOCALS~1/Temp/msohtml1/01/clip_image022.gif" shapes="_x0000_i1033" /></span><!--[if gte mso 9]><xml> <o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1033" drawaspect="Content" objectid="_1293706329"> </o:OLEObject> </xml><![endif]--><span style="mso-spacerun:yes"> </span>----------------- (iii)</span></p> <p class="MsoNormal" style="line-height:150%;tab-stops:1.0in 81.0pt"><span lang="EN-GB"><span style="position:relative;top:5.0pt;mso-text-raise:-5.0pt"><!--[if gte vml 1]><v:shape id="_x0000_i1034" type="#_x0000_t75" style="'width:105.75pt;height:18.75pt'" ole=""> <v:imagedata src="file:///C:\DOCUME~1\d8\LOCALS~1\Temp\msohtml1\01\clip_image023.wmz" title=""> </v:shape><![endif]--><img width="141" height="25" src="file:///C:/DOCUME~1/d8/LOCALS~1/Temp/msohtml1/01/clip_image024.gif" shapes="_x0000_i1034" /></span><!--[if gte mso 9]><xml> <o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1034" drawaspect="Content" objectid="_1293706330"> </o:OLEObject> </xml><![endif]--><span style="mso-spacerun:yes"> </span>---------------------- (iv)</span></p> <p class="MsoNormal" style="line-height:150%;tab-stops:1.0in 81.0pt"><span lang="EN-GB">Sub.(iii) into (iv)</span></p> <p class="MsoNormal" style="line-height:150%;tab-stops:1.0in 81.0pt"><span lang="EN-GB"><span style="position:relative;top:5.0pt;mso-text-raise:-5.0pt"><!--[if gte vml 1]><v:shape id="_x0000_i1035" type="#_x0000_t75" style="'width:219pt;height:18.75pt'" ole=""> <v:imagedata src="file:///C:\DOCUME~1\d8\LOCALS~1\Temp\msohtml1\01\clip_image025.wmz" title=""> </v:shape><![endif]--><img width="292" height="25" src="file:///C:/DOCUME~1/d8/LOCALS~1/Temp/msohtml1/01/clip_image026.gif" shapes="_x0000_i1035" /></span><!--[if gte mso 9]><xml> <o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1035" drawaspect="Content" objectid="_1293706331"> </o:OLEObject> </xml><![endif]--><span style="mso-spacerun:yes"> </span></span></p> <p class="MsoNormal" style="line-height:150%;tab-stops:1.0in 81.0pt"><span lang="EN-GB"><span style="position:relative;top:5.0pt;mso-text-raise:-5.0pt"><!--[if gte vml 1]><v:shape id="_x0000_i1036" type="#_x0000_t75" style="'width:153pt;height:17.25pt'" ole=""> <v:imagedata src="file:///C:\DOCUME~1\d8\LOCALS~1\Temp\msohtml1\01\clip_image027.wmz" title=""> </v:shape><![endif]--><img width="204" height="23" src="file:///C:/DOCUME~1/d8/LOCALS~1/Temp/msohtml1/01/clip_image028.gif" shapes="_x0000_i1036" /></span><!--[if gte mso 9]><xml> <o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1036" drawaspect="Content" objectid="_1293706332"> </o:OLEObject> </xml><![endif]--></span></p> <p class="MsoNormal" style="line-height:150%;tab-stops:1.0in 81.0pt"><span lang="EN-GB"><span style="position:relative;top:5.0pt;mso-text-raise:-5.0pt"><!--[if gte vml 1]><v:shape id="_x0000_i1037" type="#_x0000_t75" style="'width:111pt;height:17.25pt'" ole=""> <v:imagedata src="file:///C:\DOCUME~1\d8\LOCALS~1\Temp\msohtml1\01\clip_image029.wmz" title=""> </v:shape><![endif]--><img width="148" height="23" src="file:///C:/DOCUME~1/d8/LOCALS~1/Temp/msohtml1/01/clip_image030.gif" shapes="_x0000_i1037" /></span><!--[if gte mso 9]><xml> <o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1037" drawaspect="Content" objectid="_1293706333"> </o:OLEObject> </xml><![endif]--></span></p> <p class="MsoNormal" style="line-height:150%;tab-stops:1.0in 81.0pt"><span lang="EN-GB"><span style="position:relative;top:12.0pt;mso-text-raise:-12.0pt"><!--[if gte vml 1]><v:shape id="_x0000_i1038" type="#_x0000_t75" style="'width:74.25pt;height:30.75pt'" ole=""> <v:imagedata src="file:///C:\DOCUME~1\d8\LOCALS~1\Temp\msohtml1\01\clip_image031.wmz" title=""> </v:shape><![endif]--><img width="99" height="41" src="file:///C:/DOCUME~1/d8/LOCALS~1/Temp/msohtml1/01/clip_image032.gif" shapes="_x0000_i1038" /></span><!--[if gte mso 9]><xml> <o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1038" drawaspect="Content" objectid="_1293706334"> </o:OLEObject> </xml><![endif]--></span></p> <p class="MsoNormal" style="line-height:150%;tab-stops:1.0in 81.0pt"><span lang="EN-GB"><span style="position:relative;top:5.0pt;mso-text-raise:-5.0pt"><!--[if gte vml 1]><v:shape id="_x0000_i1039" type="#_x0000_t75" style="'width:69.75pt;height:17.25pt'" ole=""> <v:imagedata src="file:///C:\DOCUME~1\d8\LOCALS~1\Temp\msohtml1\01\clip_image033.wmz" title=""> </v:shape><![endif]--><img width="93" height="23" src="file:///C:/DOCUME~1/d8/LOCALS~1/Temp/msohtml1/01/clip_image034.gif" shapes="_x0000_i1039" /></span><!--[if gte mso 9]><xml> <o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1039" drawaspect="Content" objectid="_1293706335"> </o:OLEObject> </xml><![endif]--></span></p> <p class="MsoNormal" style="line-height:150%;tab-stops:1.0in 81.0pt"><span lang="EN-GB"><span style="position:relative;top:5.0pt;mso-text-raise:-5.0pt"><!--[if gte vml 1]><v:shape id="_x0000_i1040" type="#_x0000_t75" style="'width:96pt;height:17.25pt'" ole=""> <v:imagedata src="file:///C:\DOCUME~1\d8\LOCALS~1\Temp\msohtml1\01\clip_image035.wmz" title=""> </v:shape><![endif]--><img width="128" height="23" src="file:///C:/DOCUME~1/d8/LOCALS~1/Temp/msohtml1/01/clip_image036.gif" shapes="_x0000_i1040" /></span><!--[if gte mso 9]><xml> <o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1040" drawaspect="Content" objectid="_1293706336"> </o:OLEObject> </xml><![endif]--></span></p> <p class="MsoNormal" style="line-height:150%;tab-stops:1.0in 81.0pt"><span lang="EN-GB"><span style="position:relative;top:5.0pt;mso-text-raise:-5.0pt"><!--[if gte vml 1]><v:shape id="_x0000_i1041" type="#_x0000_t75" style="'width:69.75pt;height:17.25pt'" ole=""> <v:imagedata src="file:///C:\DOCUME~1\d8\LOCALS~1\Temp\msohtml1\01\clip_image037.wmz" title=""> </v:shape><![endif]--><img width="93" height="23" src="file:///C:/DOCUME~1/d8/LOCALS~1/Temp/msohtml1/01/clip_image038.gif" shapes="_x0000_i1041" /></span><!--[if gte mso 9]><xml> <o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1041" drawaspect="Content" objectid="_1293706337"> </o:OLEObject> </xml><![endif]--></span></p> <p class="MsoNormal" style="line-height:150%;tab-stops:1.0in 81.0pt"><span lang="EN-GB"><span style="position:relative;top:3.0pt;mso-text-raise:-3.0pt"><!--[if gte vml 1]><v:shape id="_x0000_i1042" type="#_x0000_t75" style="'width:45.75pt;height:14.25pt'" ole=""> <v:imagedata src="file:///C:\DOCUME~1\d8\LOCALS~1\Temp\msohtml1\01\clip_image039.wmz" title=""> </v:shape><![endif]--><img width="61" height="19" src="file:///C:/DOCUME~1/d8/LOCALS~1/Temp/msohtml1/01/clip_image040.gif" shapes="_x0000_i1042" /></span><!--[if gte mso 9]><xml> <o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1042" drawaspect="Content" objectid="_1293706338"> </o:OLEObject> </xml><![endif]--></span></p> <p class="MsoNormal" style="line-height:150%;tab-stops:1.0in 81.0pt"><span lang="EN-GB">Compound C:- </span></p> <p class="MsoNormal" style="line-height:150%;tab-stops:1.0in 81.0pt"><span lang="EN-GB"><span style="mso-tab-count:1"> </span><span style="position:relative;top:5.0pt;mso-text-raise:-5.0pt"><!--[if gte vml 1]><v:shape id="_x0000_i1043" type="#_x0000_t75" style="'width:69.75pt;height:17.25pt'" ole=""> <v:imagedata src="file:///C:\DOCUME~1\d8\LOCALS~1\Temp\msohtml1\01\clip_image041.wmz" title=""> </v:shape><![endif]--><img width="93" height="23" src="file:///C:/DOCUME~1/d8/LOCALS~1/Temp/msohtml1/01/clip_image042.gif" shapes="_x0000_i1043" /></span><!--[if gte mso 9]><xml> <o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1043" drawaspect="Content" objectid="_1293706339"> </o:OLEObject> </xml><![endif]--></span></p> <p class="MsoNormal" style="line-height:150%;tab-stops:1.0in 81.0pt"><span lang="EN-GB"><span style="mso-tab-count:1"> </span><span style="position:relative;top:5.0pt;mso-text-raise:-5.0pt"><!--[if gte vml 1]><v:shape id="_x0000_i1044" type="#_x0000_t75" style="'width:69.75pt;height:17.25pt'" ole=""> <v:imagedata src="file:///C:\DOCUME~1\d8\LOCALS~1\Temp\msohtml1\01\clip_image043.wmz" title=""> </v:shape><![endif]--><img width="93" height="23" src="file:///C:/DOCUME~1/d8/LOCALS~1/Temp/msohtml1/01/clip_image044.gif" shapes="_x0000_i1044" /></span><!--[if gte mso 9]><xml> <o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1044" drawaspect="Content" objectid="_1293706340"> </o:OLEObject> </xml><![endif]--></span></p> <p class="MsoNormal" style="line-height:150%;tab-stops:1.0in 81.0pt"><span lang="EN-GB"><span style="mso-tab-count:1"> </span><span style="position:relative;top:14.0pt;mso-text-raise:-14.0pt"><!--[if gte vml 1]><v:shape id="_x0000_i1045" type="#_x0000_t75" style="'width:66pt;height:33.75pt'" ole=""> <v:imagedata src="file:///C:\DOCUME~1\d8\LOCALS~1\Temp\msohtml1\01\clip_image045.wmz" title=""> </v:shape><![endif]--><img width="88" height="45" src="file:///C:/DOCUME~1/d8/LOCALS~1/Temp/msohtml1/01/clip_image046.gif" shapes="_x0000_i1045" /></span><!--[if gte mso 9]><xml> <o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1045" drawaspect="Content" objectid="_1293706341"> </o:OLEObject> </xml><![endif]--></span></p> <p class="MsoNormal" style="line-height:150%;tab-stops:1.0in 81.0pt"><span lang="EN-GB">Compound A:-</span></p> <p class="MsoNormal" style="line-height:150%;tab-stops:1.0in 81.0pt"><span lang="EN-GB"><span style="mso-tab-count:1"> </span><span style="position:relative;top:5.0pt;mso-text-raise:-5.0pt"><!--[if gte vml 1]><v:shape id="_x0000_i1046" type="#_x0000_t75" style="'width:69.75pt;height:17.25pt'" ole=""> <v:imagedata src="file:///C:\DOCUME~1\d8\LOCALS~1\Temp\msohtml1\01\clip_image047.wmz" title=""> </v:shape><![endif]--><img width="93" height="23" src="file:///C:/DOCUME~1/d8/LOCALS~1/Temp/msohtml1/01/clip_image048.gif" shapes="_x0000_i1046" /></span><!--[if gte mso 9]><xml> <o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1046" drawaspect="Content" objectid="_1293706342"> </o:OLEObject> </xml><![endif]--></span></p> <p class="MsoNormal" style="line-height:150%;tab-stops:1.0in 81.0pt"><span lang="EN-GB"><span style="mso-tab-count:1"> </span><span style="position:relative;top:5.0pt;mso-text-raise:-5.0pt"><!--[if gte vml 1]><v:shape id="_x0000_i1047" type="#_x0000_t75" style="'width:69.75pt;height:17.25pt'" ole=""> <v:imagedata src="file:///C:\DOCUME~1\d8\LOCALS~1\Temp\msohtml1\01\clip_image049.wmz" title=""> </v:shape><![endif]--><img width="93" height="23" src="file:///C:/DOCUME~1/d8/LOCALS~1/Temp/msohtml1/01/clip_image050.gif" shapes="_x0000_i1047" /></span><!--[if gte mso 9]><xml> <o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1047" drawaspect="Content" objectid="_1293706343"> </o:OLEObject> </xml><![endif]--></span></p> <p class="MsoNormal" style="line-height:150%;tab-stops:1.0in 81.0pt"><span lang="EN-GB"><span style="mso-tab-count:1"> </span><span style="position:relative;top:3.0pt;mso-text-raise:-3.0pt"><!--[if gte vml 1]><v:shape id="_x0000_i1048" type="#_x0000_t75" style="'width:53.25pt;height:14.25pt'" ole=""> <v:imagedata src="file:///C:\DOCUME~1\d8\LOCALS~1\Temp\msohtml1\01\clip_image051.wmz" title=""> </v:shape><![endif]--><img width="71" height="19" src="file:///C:/DOCUME~1/d8/LOCALS~1/Temp/msohtml1/01/clip_image052.gif" shapes="_x0000_i1048" /></span><!--[if gte mso 9]><xml> <o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1048" drawaspect="Content" objectid="_1293706344"> </o:OLEObject> </xml><![endif]--></span></p>d8http://www.blogger.com/profile/09390427562617157781noreply@blogger.com1tag:blogger.com,1999:blog-6305446887053345257.post-19819166623045481152009-01-08T17:30:00.000-08:002009-01-16T22:00:12.645-08:00Experiment<p class="MsoNormal" style="line-height:150%;tab-stops:1.0in 81.0pt"><br /></p> <p class="MsoNormal" style="line-height:150%;tab-stops:1.0in 81.0pt"><span lang="EN-GB"><o:p> </o:p></span></p> <p class="MsoNormal" style="line-height:150%;tab-stops:1.0in 81.0pt"><span lang="EN-GB">Pendulum swing</span></p> <table class="MsoTableGrid" border="1" cellspacing="0" cellpadding="0" style="border-collapse:collapse;border:none;mso-border-alt:solid windowtext .5pt; mso-yfti-tbllook:480;mso-padding-alt:0in 5.4pt 0in 5.4pt;mso-border-insideh: .5pt solid windowtext;mso-border-insidev:.5pt solid windowtext"> <tbody><tr style="mso-yfti-irow:0;mso-yfti-firstrow:yes"> <td width="93" valign="top" style="width:69.85pt;border:solid windowtext 1.0pt; mso-border-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"> <p class="MsoNormal" align="center" style="text-align:center;line-height:150%; tab-stops:1.0in 81.0pt"><span lang="EN-GB">Type</span></p> </td> <td width="68" valign="top" style="width:50.9pt;border:solid windowtext 1.0pt; border-left:none;mso-border-left-alt:solid windowtext .5pt;mso-border-alt: solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"> <p class="MsoNormal" align="center" style="text-align:center;line-height:150%; tab-stops:1.0in 81.0pt"><span lang="EN-GB" style="font-family:Symbol; mso-ascii-font-family:"Times New Roman";mso-hansi-font-family:"Times New Roman"; mso-char-type:symbol;mso-symbol-font-family:Symbol"><span style="mso-char-type: symbol;mso-symbol-font-family:Symbol">q</span></span></p> </td> <td width="133" colspan="2" valign="top" style="width:100.1pt;border:solid windowtext 1.0pt; border-left:none;mso-border-left-alt:solid windowtext .5pt;mso-border-alt: solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"> <p class="MsoNormal" align="center" style="text-align:center;line-height:150%; tab-stops:1.0in 81.0pt"><span lang="EN-GB">Smaller side at top, s</span></p> </td> <td width="69" valign="top" style="width:51.45pt;border:solid windowtext 1.0pt; border-left:none;mso-border-left-alt:solid windowtext .5pt;mso-border-alt: solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"> <p class="MsoNormal" align="center" style="text-align:center;line-height:150%; tab-stops:1.0in 81.0pt"><span lang="EN-GB">Average</span></p> <p class="MsoNormal" align="center" style="text-align:center;line-height:150%; tab-stops:1.0in 81.0pt"><span lang="EN-GB">Reading, s</span></p> </td> <td width="136" colspan="2" valign="top" style="width:101.85pt;border:solid windowtext 1.0pt; border-left:none;mso-border-left-alt:solid windowtext .5pt;mso-border-alt: solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"> <p class="MsoNormal" align="center" style="text-align:center;line-height:150%; tab-stops:1.0in 81.0pt"><span lang="EN-GB">Larger side at top, s</span></p> </td> <td width="69" valign="top" style="width:51.95pt;border:solid windowtext 1.0pt; border-left:none;mso-border-left-alt:solid windowtext .5pt;mso-border-alt: solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"> <p class="MsoNormal" align="center" style="text-align:center;line-height:150%; tab-stops:1.0in 81.0pt"><span lang="EN-GB">Average reading, s</span></p> </td> </tr> <tr style="mso-yfti-irow:1"> <td width="93" valign="top" style="width:69.85pt;border:solid windowtext 1.0pt; border-top:none;mso-border-top-alt:solid windowtext .5pt;mso-border-alt:solid windowtext .5pt; padding:0in 5.4pt 0in 5.4pt"> <p class="MsoNormal" style="line-height:150%;tab-stops:1.0in 81.0pt"><span lang="EN-GB">Rounded Rod</span></p> </td> <td width="68" valign="top" style="width:50.9pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt; mso-border-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"> <p class="MsoNormal" align="center" style="text-align:center;line-height:150%; tab-stops:1.0in 81.0pt"><span lang="EN-GB"><span style="position:relative; top:3.0pt;mso-text-raise:-3.0pt"><!--[if gte vml 1]><v:shapetype id="_x0000_t75" coordsize="21600,21600" spt="75" preferrelative="t" path="m@4@5l@4@11@9@11@9@5xe" filled="f" stroked="f"> <v:stroke joinstyle="miter"> <v:formulas> <v:f eqn="if lineDrawn pixelLineWidth 0"> <v:f eqn="sum @0 1 0"> <v:f eqn="sum 0 0 @1"> <v:f eqn="prod @2 1 2"> <v:f eqn="prod @3 21600 pixelWidth"> <v:f eqn="prod @3 21600 pixelHeight"> <v:f eqn="sum @0 0 1"> <v:f eqn="prod @6 1 2"> <v:f eqn="prod @7 21600 pixelWidth"> <v:f eqn="sum @8 21600 0"> <v:f eqn="prod @7 21600 pixelHeight"> <v:f eqn="sum @10 21600 0"> </v:formulas> <v:path extrusionok="f" gradientshapeok="t" connecttype="rect"> <o:lock ext="edit" aspectratio="t"> </v:shapetype><v:shape id="_x0000_i1032" type="#_x0000_t75" style="'width:18pt;" ole=""> <v:imagedata src="file:///C:\DOCUME~1\d8\LOCALS~1\Temp\msohtml1\01\clip_image001.wmz" title=""> </v:shape><![endif]--><img width="24" height="21" src="file:///C:/DOCUME~1/d8/LOCALS~1/Temp/msohtml1/01/clip_image002.gif" shapes="_x0000_i1032" /></span><!--[if gte mso 9]><xml> <o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1032" drawaspect="Content" objectid="_1293706243"> </o:OLEObject> </xml><![endif]-->.</span></p> </td> <td width="74" valign="top" style="width:55.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt; mso-border-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"> <p class="MsoNormal" align="center" style="text-align:center;line-height:150%; tab-stops:1.0in 81.0pt"><span lang="EN-GB">9.06</span></p> </td> <td width="59" valign="top" style="width:44.45pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt; mso-border-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"> <p class="MsoNormal" align="center" style="text-align:center;line-height:150%; tab-stops:1.0in 81.0pt"><span lang="EN-GB">8.91</span></p> </td> <td width="69" valign="top" style="width:51.45pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt; mso-border-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"> <p class="MsoNormal" align="center" style="text-align:center;line-height:150%; tab-stops:1.0in 81.0pt"><span lang="EN-GB">8.99</span></p> </td> <td width="68" valign="top" style="width:50.9pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt; mso-border-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"> <p class="MsoNormal" align="center" style="text-align:center;line-height:150%; tab-stops:1.0in 81.0pt"><span lang="EN-GB">8.72</span></p> </td> <td width="68" valign="top" style="width:50.95pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt; mso-border-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"> <p class="MsoNormal" align="center" style="text-align:center;line-height:150%; tab-stops:1.0in 81.0pt"><span lang="EN-GB">8.68</span></p> </td> <td width="69" valign="top" style="width:51.95pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt; mso-border-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"> <p class="MsoNormal" align="center" style="text-align:center;line-height:150%; tab-stops:1.0in 81.0pt"><span lang="EN-GB">8.70</span></p> </td> </tr> <tr style="mso-yfti-irow:2"> <td width="93" valign="top" style="width:69.85pt;border:solid windowtext 1.0pt; border-top:none;mso-border-top-alt:solid windowtext .5pt;mso-border-alt:solid windowtext .5pt; padding:0in 5.4pt 0in 5.4pt"> <p class="MsoNormal" style="line-height:150%;tab-stops:1.0in 81.0pt"><span lang="EN-GB">Rectangular Rod</span></p> </td> <td width="68" valign="top" style="width:50.9pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt; mso-border-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"> <p class="MsoNormal" align="center" style="text-align:center;line-height:150%; tab-stops:1.0in 81.0pt"><span lang="EN-GB"><span style="position:relative; top:3.0pt;mso-text-raise:-3.0pt"><!--[if gte vml 1]><v:shape id="_x0000_i1033" type="#_x0000_t75" style="'width:18pt;height:15.75pt'" ole=""> <v:imagedata src="file:///C:\DOCUME~1\d8\LOCALS~1\Temp\msohtml1\01\clip_image001.wmz" title=""> </v:shape><![endif]--><img width="24" height="21" src="file:///C:/DOCUME~1/d8/LOCALS~1/Temp/msohtml1/01/clip_image002.gif" shapes="_x0000_i1033" /></span><!--[if gte mso 9]><xml> <o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1033" drawaspect="Content" objectid="_1293706244"> </o:OLEObject> </xml><![endif]-->.</span></p> </td> <td width="74" valign="top" style="width:55.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt; mso-border-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"> <p class="MsoNormal" align="center" style="text-align:center;line-height:150%; tab-stops:1.0in 81.0pt"><span lang="EN-GB">8.22</span></p> </td> <td width="59" valign="top" style="width:44.45pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt; mso-border-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"> <p class="MsoNormal" align="center" style="text-align:center;line-height:150%; tab-stops:1.0in 81.0pt"><span lang="EN-GB">8.65</span></p> </td> <td width="69" valign="top" style="width:51.45pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt; mso-border-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"> <p class="MsoNormal" align="center" style="text-align:center;line-height:150%; tab-stops:1.0in 81.0pt"><span lang="EN-GB">8.44</span></p> </td> <td width="68" valign="top" style="width:50.9pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt; mso-border-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"> <p class="MsoNormal" align="center" style="text-align:center;line-height:150%; tab-stops:1.0in 81.0pt"><span lang="EN-GB">8.40</span></p> </td> <td width="68" valign="top" style="width:50.95pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt; mso-border-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"> <p class="MsoNormal" align="center" style="text-align:center;line-height:150%; tab-stops:1.0in 81.0pt"><span lang="EN-GB">8.43</span></p> </td> <td width="69" valign="top" style="width:51.95pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt; mso-border-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"> <p class="MsoNormal" align="center" style="text-align:center;line-height:150%; tab-stops:1.0in 81.0pt"><span lang="EN-GB">8.42</span></p> </td> </tr> <tr style="mso-yfti-irow:3;mso-yfti-lastrow:yes"> <td width="93" valign="top" style="width:69.85pt;border:solid windowtext 1.0pt; border-top:none;mso-border-top-alt:solid windowtext .5pt;mso-border-alt:solid windowtext .5pt; padding:0in 5.4pt 0in 5.4pt"> <p class="MsoNormal" style="line-height:150%;tab-stops:1.0in 81.0pt"><span lang="EN-GB">Prismatic Thick Place</span></p> </td> <td width="68" valign="top" style="width:50.9pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt; mso-border-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"> <p class="MsoNormal" align="center" style="text-align:center;line-height:150%; tab-stops:1.0in 81.0pt"><span lang="EN-GB"><span style="position:relative; top:3.0pt;mso-text-raise:-3.0pt"><!--[if gte vml 1]><v:shape id="_x0000_i1034" type="#_x0000_t75" style="'width:18pt;height:15.75pt'" ole=""> <v:imagedata src="file:///C:\DOCUME~1\d8\LOCALS~1\Temp\msohtml1\01\clip_image001.wmz" title=""> </v:shape><![endif]--><img width="24" height="21" src="file:///C:/DOCUME~1/d8/LOCALS~1/Temp/msohtml1/01/clip_image002.gif" shapes="_x0000_i1034" /></span><!--[if gte mso 9]><xml> <o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1034" drawaspect="Content" objectid="_1293706245"> </o:OLEObject> </xml><![endif]-->.</span></p> </td> <td width="74" valign="top" style="width:55.65pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt; mso-border-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"> <p class="MsoNormal" align="center" style="text-align:center;line-height:150%; tab-stops:1.0in 81.0pt"><span lang="EN-GB">9.47</span></p> </td> <td width="59" valign="top" style="width:44.45pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt; mso-border-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"> <p class="MsoNormal" align="center" style="text-align:center;line-height:150%; tab-stops:1.0in 81.0pt"><span lang="EN-GB">9.08</span></p> </td> <td width="69" valign="top" style="width:51.45pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt; mso-border-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"> <p class="MsoNormal" align="center" style="text-align:center;line-height:150%; tab-stops:1.0in 81.0pt"><span lang="EN-GB">9.28</span></p> </td> <td width="68" valign="top" style="width:50.9pt;border-top:none;border-left:none; border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt; mso-border-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"> <p class="MsoNormal" align="center" style="text-align:center;line-height:150%; tab-stops:1.0in 81.0pt"><span lang="EN-GB">8.53</span></p> </td> <td width="68" valign="top" style="width:50.95pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt; mso-border-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"> <p class="MsoNormal" align="center" style="text-align:center;line-height:150%; tab-stops:1.0in 81.0pt"><span lang="EN-GB">8.28</span></p> </td> <td width="69" valign="top" style="width:51.95pt;border-top:none;border-left: none;border-bottom:solid windowtext 1.0pt;border-right:solid windowtext 1.0pt; mso-border-top-alt:solid windowtext .5pt;mso-border-left-alt:solid windowtext .5pt; mso-border-alt:solid windowtext .5pt;padding:0in 5.4pt 0in 5.4pt"> <p class="MsoNormal" align="center" style="text-align:center;line-height:150%; tab-stops:1.0in 81.0pt"><span lang="EN-GB">8.41</span></p> </td> </tr> </tbody></table> <p class="MsoNormal" style="line-height:150%;tab-stops:1.0in 81.0pt"><span lang="EN-GB"><o:p> </o:p></span></p> <p class="MsoNormal" style="line-height:150%;tab-stops:1.0in 81.0pt"><u><span lang="EN-GB">For Compound B (Rectangular Rod)<o:p></o:p></span></u></p> <p class="MsoNormal" style="line-height:150%;tab-stops:1.0in 81.0pt"><u><span lang="EN-GB"><o:p><span style="text-decoration:none"> </span></o:p></span></u></p> <p class="MsoNormal" style="line-height:150%;tab-stops:1.0in 81.0pt"><span lang="EN-GB"><span style="position:relative;top:16.0pt;mso-text-raise:-16.0pt"><!--[if gte vml 1]><v:shape id="_x0000_i1025" type="#_x0000_t75" style="'width:93pt;height:39.75pt'" ole=""> <v:imagedata src="file:///C:\DOCUME~1\d8\LOCALS~1\Temp\msohtml1\01\clip_image003.wmz" title=""> </v:shape><![endif]--><img width="124" height="53" src="file:///C:/DOCUME~1/d8/LOCALS~1/Temp/msohtml1/01/clip_image004.gif" shapes="_x0000_i1025" /></span><!--[if gte mso 9]><xml> <o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1025" drawaspect="Content" objectid="_1293706247"> </o:OLEObject> </xml><![endif]--></span></p> <p class="MsoNormal" style="line-height:150%;tab-stops:1.0in 81.0pt"><span lang="EN-GB"><span style="position:relative;top:16.0pt;mso-text-raise:-16.0pt"><!--[if gte vml 1]><v:shape id="_x0000_i1029" type="#_x0000_t75" style="'width:152.25pt;height:39pt'" ole=""> <v:imagedata src="file:///C:\DOCUME~1\d8\LOCALS~1\Temp\msohtml1\01\clip_image005.wmz" title=""> </v:shape><![endif]--><img width="203" height="52" src="file:///C:/DOCUME~1/d8/LOCALS~1/Temp/msohtml1/01/clip_image006.gif" shapes="_x0000_i1029" /></span><!--[if gte mso 9]><xml> <o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1029" drawaspect="Content" objectid="_1293706248"> </o:OLEObject> </xml><![endif]--></span></p> <p class="MsoNormal" style="line-height:150%;tab-stops:1.0in 81.0pt"><span lang="EN-GB"><span style="position:relative;top:16.0pt;mso-text-raise:-16.0pt"><!--[if gte vml 1]><v:shape id="_x0000_i1026" type="#_x0000_t75" style="'width:120pt;height:39pt'" ole=""> <v:imagedata src="file:///C:\DOCUME~1\d8\LOCALS~1\Temp\msohtml1\01\clip_image007.wmz" title=""> </v:shape><![endif]--><img width="160" height="52" src="file:///C:/DOCUME~1/d8/LOCALS~1/Temp/msohtml1/01/clip_image008.gif" shapes="_x0000_i1026" /></span><!--[if gte mso 9]><xml> <o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1026" drawaspect="Content" objectid="_1293706249"> </o:OLEObject> </xml><![endif]--></span></p> <p class="MsoNormal" style="line-height:150%;tab-stops:1.0in 81.0pt"><span lang="EN-GB"><span style="position:relative;top:16.0pt;mso-text-raise:-16.0pt"><!--[if gte vml 1]><v:shape id="_x0000_i1027" type="#_x0000_t75" style="'width:99pt;height:39pt'" ole=""> <v:imagedata src="file:///C:\DOCUME~1\d8\LOCALS~1\Temp\msohtml1\01\clip_image009.wmz" title=""> </v:shape><![endif]--><img width="132" height="52" src="file:///C:/DOCUME~1/d8/LOCALS~1/Temp/msohtml1/01/clip_image010.gif" shapes="_x0000_i1027" /></span><!--[if gte mso 9]><xml> <o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1027" drawaspect="Content" objectid="_1293706250"> </o:OLEObject> </xml><![endif]--></span></p> <p class="MsoNormal" style="line-height:150%;tab-stops:1.0in 81.0pt"><span lang="EN-GB"><span style="position:relative;top:15.0pt;mso-text-raise:-15.0pt"><!--[if gte vml 1]><v:shape id="_x0000_i1028" type="#_x0000_t75" style="'width:83.25pt;height:36pt'" ole=""> <v:imagedata src="file:///C:\DOCUME~1\d8\LOCALS~1\Temp\msohtml1\01\clip_image011.wmz" title=""> </v:shape><![endif]--><img width="111" height="48" src="file:///C:/DOCUME~1/d8/LOCALS~1/Temp/msohtml1/01/clip_image012.gif" shapes="_x0000_i1028" /></span><!--[if gte mso 9]><xml> <o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1028" drawaspect="Content" objectid="_1293706251"> </o:OLEObject> </xml><![endif]--></span></p> <p class="MsoNormal" style="line-height:150%;tab-stops:1.0in 81.0pt"><span lang="EN-GB"><o:p> </o:p></span></p> <p class="MsoNormal" style="line-height:150%;tab-stops:1.0in 81.0pt"><span lang="EN-GB"><o:p> </o:p></span></p> <p class="MsoNormal" style="line-height:150%;tab-stops:1.0in 81.0pt"><span lang="EN-GB"><span style="position:relative;top:5.0pt;mso-text-raise:-5.0pt"><!--[if gte vml 1]><v:shape id="_x0000_i1035" type="#_x0000_t75" style="'width:99.75pt;height:18.75pt'" ole=""> <v:imagedata src="file:///C:\DOCUME~1\d8\LOCALS~1\Temp\msohtml1\01\clip_image013.wmz" title=""> </v:shape><![endif]--><img width="133" height="25" src="file:///C:/DOCUME~1/d8/LOCALS~1/Temp/msohtml1/01/clip_image014.gif" shapes="_x0000_i1035" /></span><!--[if gte mso 9]><xml> <o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1035" drawaspect="Content" objectid="_1293706252"> </o:OLEObject> </xml><![endif]--></span></p> <p class="MsoNormal" style="line-height:150%;tab-stops:1.0in 81.0pt"><span lang="EN-GB"><span style="position:relative;top:5.0pt;mso-text-raise:-5.0pt"><!--[if gte vml 1]><v:shape id="_x0000_i1036" type="#_x0000_t75" style="'width:99pt;height:18.75pt'" ole=""> <v:imagedata src="file:///C:\DOCUME~1\d8\LOCALS~1\Temp\msohtml1\01\clip_image015.wmz" title=""> </v:shape><![endif]--><img width="132" height="25" src="file:///C:/DOCUME~1/d8/LOCALS~1/Temp/msohtml1/01/clip_image016.gif" shapes="_x0000_i1036" /></span><!--[if gte mso 9]><xml> <o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1036" drawaspect="Content" objectid="_1293706253"> </o:OLEObject> </xml><![endif]-->---------------- (i)</span></p> <p class="MsoNormal" style="line-height:150%;tab-stops:1.0in 81.0pt"><span lang="EN-GB"><span style="position:relative;top:5.0pt;mso-text-raise:-5.0pt"><!--[if gte vml 1]><v:shape id="_x0000_i1031" type="#_x0000_t75" style="'width:74.25pt;height:17.25pt'" ole=""> <v:imagedata src="file:///C:\DOCUME~1\d8\LOCALS~1\Temp\msohtml1\01\clip_image017.wmz" title=""> </v:shape><![endif]--><img width="99" height="23" src="file:///C:/DOCUME~1/d8/LOCALS~1/Temp/msohtml1/01/clip_image018.gif" shapes="_x0000_i1031" /></span><!--[if gte mso 9]><xml> <o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1031" drawaspect="Content" objectid="_1293706254"> </o:OLEObject> </xml><![endif]--></span></p> <p class="MsoNormal" style="line-height:150%;tab-stops:1.0in 81.0pt"><span lang="EN-GB"><span style="position:relative;top:5.0pt;mso-text-raise:-5.0pt"><!--[if gte vml 1]><v:shape id="_x0000_i1037" type="#_x0000_t75" style="'width:72.75pt;height:17.25pt'" ole=""> <v:imagedata src="file:///C:\DOCUME~1\d8\LOCALS~1\Temp\msohtml1\01\clip_image019.wmz" title=""> </v:shape><![endif]--><img width="97" height="23" src="file:///C:/DOCUME~1/d8/LOCALS~1/Temp/msohtml1/01/clip_image020.gif" shapes="_x0000_i1037" /></span><!--[if gte mso 9]><xml> <o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1037" drawaspect="Content" objectid="_1293706255"> </o:OLEObject> </xml><![endif]--><span style="mso-tab-count:1"> </span><span style="mso-spacerun:yes"> </span>----------------- (ii)</span></p> <p class="MsoNormal" style="line-height:150%;tab-stops:1.0in 81.0pt"><span lang="EN-GB">Subs. (ii) into (i)</span></p> <p class="MsoNormal" style="line-height:150%;tab-stops:1.0in 81.0pt"><span lang="EN-GB"><span style="position:relative;top:5.0pt;mso-text-raise:-5.0pt"><!--[if gte vml 1]><v:shape id="_x0000_i1038" type="#_x0000_t75" style="'width:152.25pt;height:18.75pt'" ole=""> <v:imagedata src="file:///C:\DOCUME~1\d8\LOCALS~1\Temp\msohtml1\01\clip_image021.wmz" title=""> </v:shape><![endif]--><img width="203" height="25" src="file:///C:/DOCUME~1/d8/LOCALS~1/Temp/msohtml1/01/clip_image022.gif" shapes="_x0000_i1038" /></span><!--[if gte mso 9]><xml> <o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1038" drawaspect="Content" objectid="_1293706256"> </o:OLEObject> </xml><![endif]--><span style="mso-spacerun:yes"> </span>----------------- (iii)</span></p> <p class="MsoNormal" style="line-height:150%;tab-stops:1.0in 81.0pt"><span lang="EN-GB"><span style="position:relative;top:16.0pt;mso-text-raise:-16.0pt"><!--[if gte vml 1]><v:shape id="_x0000_i1030" type="#_x0000_t75" style="'width:158.25pt;height:39.75pt'" ole=""> <v:imagedata src="file:///C:\DOCUME~1\d8\LOCALS~1\Temp\msohtml1\01\clip_image023.wmz" title=""> </v:shape><![endif]--><img width="211" height="53" src="file:///C:/DOCUME~1/d8/LOCALS~1/Temp/msohtml1/01/clip_image024.gif" shapes="_x0000_i1030" /></span><!--[if gte mso 9]><xml> <o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1030" drawaspect="Content" objectid="_1293706257"> </o:OLEObject> </xml><![endif]--></span></p> <p class="MsoNormal" style="line-height:150%;tab-stops:1.0in 81.0pt"><span lang="EN-GB"><span style="position:relative;top:16.0pt;mso-text-raise:-16.0pt"><!--[if gte vml 1]><v:shape id="_x0000_i1039" type="#_x0000_t75" style="'width:99pt;height:39pt'" ole=""> <v:imagedata src="file:///C:\DOCUME~1\d8\LOCALS~1\Temp\msohtml1\01\clip_image025.wmz" title=""> </v:shape><![endif]--><img width="132" height="52" src="file:///C:/DOCUME~1/d8/LOCALS~1/Temp/msohtml1/01/clip_image026.gif" shapes="_x0000_i1039" /></span><!--[if gte mso 9]><xml> <o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1039" drawaspect="Content" objectid="_1293706258"> </o:OLEObject> </xml><![endif]--></span></p> <p class="MsoNormal" style="line-height:150%;tab-stops:1.0in 81.0pt"><span lang="EN-GB"><span style="position:relative;top:15.0pt;mso-text-raise:-15.0pt"><!--[if gte vml 1]><v:shape id="_x0000_i1040" type="#_x0000_t75" style="'width:93.75pt;height:39pt'" ole=""> <v:imagedata src="file:///C:\DOCUME~1\d8\LOCALS~1\Temp\msohtml1\01\clip_image027.wmz" title=""> </v:shape><![endif]--><img width="125" height="52" src="file:///C:/DOCUME~1/d8/LOCALS~1/Temp/msohtml1/01/clip_image028.gif" shapes="_x0000_i1040" /></span><!--[if gte mso 9]><xml> <o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1040" drawaspect="Content" objectid="_1293706259"> </o:OLEObject> </xml><![endif]--></span></p> <p class="MsoNormal" style="line-height:150%;tab-stops:1.0in 81.0pt"><span lang="EN-GB"><span style="position:relative;top:5.0pt;mso-text-raise:-5.0pt"><!--[if gte vml 1]><v:shape id="_x0000_i1041" type="#_x0000_t75" style="'width:92.25pt;height:18.75pt'" ole=""> <v:imagedata src="file:///C:\DOCUME~1\d8\LOCALS~1\Temp\msohtml1\01\clip_image029.wmz" title=""> </v:shape><![endif]--><img width="123" height="25" src="file:///C:/DOCUME~1/d8/LOCALS~1/Temp/msohtml1/01/clip_image030.gif" shapes="_x0000_i1041" /></span><!--[if gte mso 9]><xml> <o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1041" drawaspect="Content" objectid="_1293706260"> </o:OLEObject> </xml><![endif]--><span style="mso-tab-count:1"> </span>-------------- (iv)</span></p> <p class="MsoNormal" style="line-height:150%;tab-stops:1.0in 81.0pt"><span lang="EN-GB"><o:p> </o:p></span></p> <p class="MsoNormal" style="line-height:150%;tab-stops:1.0in 81.0pt"><span lang="EN-GB">Subst. (iii) into (iv)</span></p> <p class="MsoNormal" style="line-height:150%;tab-stops:1.0in 81.0pt"><span lang="EN-GB"><span style="position:relative;top:5.0pt;mso-text-raise:-5.0pt"><!--[if gte vml 1]><v:shape id="_x0000_i1042" type="#_x0000_t75" style="'width:197.25pt;height:17.25pt'" ole=""> <v:imagedata src="file:///C:\DOCUME~1\d8\LOCALS~1\Temp\msohtml1\01\clip_image031.wmz" title=""> </v:shape><![endif]--><img width="263" height="23" src="file:///C:/DOCUME~1/d8/LOCALS~1/Temp/msohtml1/01/clip_image032.gif" shapes="_x0000_i1042" /></span><!--[if gte mso 9]><xml> <o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1042" drawaspect="Content" objectid="_1293706261"> </o:OLEObject> </xml><![endif]--></span></p> <p class="MsoNormal" style="line-height:150%;tab-stops:1.0in 81.0pt"><span lang="EN-GB"><span style="position:relative;top:5.0pt;mso-text-raise:-5.0pt"><!--[if gte vml 1]><v:shape id="_x0000_i1043" type="#_x0000_t75" style="'width:153pt;height:17.25pt'" ole=""> <v:imagedata src="file:///C:\DOCUME~1\d8\LOCALS~1\Temp\msohtml1\01\clip_image033.wmz" title=""> </v:shape><![endif]--><img width="204" height="23" src="file:///C:/DOCUME~1/d8/LOCALS~1/Temp/msohtml1/01/clip_image034.gif" shapes="_x0000_i1043" /></span><!--[if gte mso 9]><xml> <o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1043" drawaspect="Content" objectid="_1293706262"> </o:OLEObject> </xml><![endif]--></span></p> <p class="MsoNormal" style="line-height:150%;tab-stops:1.0in 81.0pt"><span lang="EN-GB"><span style="position:relative;top:5.0pt;mso-text-raise:-5.0pt"><!--[if gte vml 1]><v:shape id="_x0000_i1044" type="#_x0000_t75" style="'width:111pt;height:17.25pt'" ole=""> <v:imagedata src="file:///C:\DOCUME~1\d8\LOCALS~1\Temp\msohtml1\01\clip_image035.wmz" title=""> </v:shape><![endif]--><img width="148" height="23" src="file:///C:/DOCUME~1/d8/LOCALS~1/Temp/msohtml1/01/clip_image036.gif" shapes="_x0000_i1044" /></span><!--[if gte mso 9]><xml> <o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1044" drawaspect="Content" objectid="_1293706263"> </o:OLEObject> </xml><![endif]--></span></p> <p class="MsoNormal" style="line-height:150%;tab-stops:1.0in 81.0pt"><span lang="EN-GB"><span style="position:relative;top:5.0pt;mso-text-raise:-5.0pt"><!--[if gte vml 1]><v:shape id="_x0000_i1045" type="#_x0000_t75" style="'width:69.75pt;height:17.25pt'" ole=""> <v:imagedata src="file:///C:\DOCUME~1\d8\LOCALS~1\Temp\msohtml1\01\clip_image037.wmz" title=""> </v:shape><![endif]--><img width="93" height="23" src="file:///C:/DOCUME~1/d8/LOCALS~1/Temp/msohtml1/01/clip_image038.gif" shapes="_x0000_i1045" /></span><!--[if gte mso 9]><xml> <o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1045" drawaspect="Content" objectid="_1293706264"> </o:OLEObject> </xml><![endif]--></span></p> <p class="MsoNormal" style="line-height:150%;tab-stops:1.0in 81.0pt"><span lang="EN-GB"><span style="position:relative;top:5.0pt;mso-text-raise:-5.0pt"><!--[if gte vml 1]><v:shape id="_x0000_i1046" type="#_x0000_t75" style="'width:69.75pt;height:17.25pt'" ole=""> <v:imagedata src="file:///C:\DOCUME~1\d8\LOCALS~1\Temp\msohtml1\01\clip_image039.wmz" title=""> </v:shape><![endif]--><img width="93" height="23" src="file:///C:/DOCUME~1/d8/LOCALS~1/Temp/msohtml1/01/clip_image040.gif" shapes="_x0000_i1046" /></span><!--[if gte mso 9]><xml> <o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1046" drawaspect="Content" objectid="_1293706265"> </o:OLEObject> </xml><![endif]--></span></p>d8http://www.blogger.com/profile/09390427562617157781noreply@blogger.com0tag:blogger.com,1999:blog-6305446887053345257.post-29795840941287839542009-01-07T16:35:00.000-08:002009-01-16T21:56:17.247-08:00Diagrams<p class="MsoNormal" style="line-height:150%;tab-stops:1.0in 81.0pt"><br /></p> <p class="MsoNormal" style="line-height:150%;tab-stops:1.0in 81.0pt"><span lang="EN-GB"><o:p> </o:p></span></p> <p class="MsoNormal" style="line-height:150%;tab-stops:1.0in 81.0pt"><span lang="EN-GB"><o:p> </o:p></span></p> <p class="MsoNormal" style="line-height:150%;tab-stops:1.0in 81.0pt"><!--[if mso & !supportInlineShapes & supportFields]><span lang="EN-GB"><span style="'mso-element:field-begin;mso-field-lock:yes'"></span><span style="'mso-spacerun:yes'"> </span>SHAPE<span style="'mso-spacerun:yes'"> </span>\* MERGEFORMAT <span style="'mso-element:field-separator'"></span></span><![endif]--><span lang="EN-GB"><!--[if gte vml 1]><v:group id="_x0000_s1026" editas="canvas" style="'width:414pt;height:279pt;mso-position-horizontal-relative:char;" coordorigin="2360,9120" coordsize="7200,4960"> <o:lock ext="edit" aspectratio="t"> <v:shapetype id="_x0000_t75" coordsize="21600,21600" spt="75" preferrelative="t" path="m@4@5l@4@11@9@11@9@5xe" filled="f" stroked="f"> <v:stroke joinstyle="miter"> <v:formulas> <v:f eqn="if lineDrawn pixelLineWidth 0"> <v:f eqn="sum @0 1 0"> <v:f eqn="sum 0 0 @1"> <v:f eqn="prod @2 1 2"> <v:f eqn="prod @3 21600 pixelWidth"> <v:f eqn="prod @3 21600 pixelHeight"> <v:f eqn="sum @0 0 1"> <v:f eqn="prod @6 1 2"> <v:f eqn="prod @7 21600 pixelWidth"> <v:f eqn="sum @8 21600 0"> <v:f eqn="prod @7 21600 pixelHeight"> <v:f eqn="sum @10 21600 0"> </v:formulas> <v:path extrusionok="f" gradientshapeok="t" connecttype="rect"> <o:lock ext="edit" aspectratio="t"> </v:shapetype><v:shape id="_x0000_s1027" type="#_x0000_t75" style="'position:absolute;" preferrelative="f"> <v:fill detectmouseclick="t"> <v:path extrusionok="t" connecttype="none"> <o:lock ext="edit" text="t"> </v:shape><v:oval id="_x0000_s1028" style="'position:absolute;left:2517;top:9280;"> <v:oval id="_x0000_s1029" style="'position:absolute;left:2673;top:9440;width:1250;"> <v:oval id="_x0000_s1030" style="'position:absolute;left:7525;top:9600;width:1096;"> <v:oval id="_x0000_s1031" style="'position:absolute;left:7682;top:9760;width:780;"> <v:line id="_x0000_s1032" style="'position:absolute'" from="4082,9920" to="6273,9920"> <v:line id="_x0000_s1033" style="'position:absolute'" from="4082,10240" to="6273,10240"> <v:line id="_x0000_s1034" style="'position:absolute'" from="6117,9920" to="7525,9920"> <v:line id="_x0000_s1035" style="'position:absolute'" from="6117,10240" to="7525,10240"> <v:oval id="_x0000_s1036" style="'position:absolute;left:2517;top:9280;width:1563;"> <v:oval id="_x0000_s1037" style="'position:absolute;left:2673;top:9440;width:1252;"> <v:oval id="_x0000_s1038" style="'position:absolute;left:2673;top:11520;"> <v:oval id="_x0000_s1039" style="'position:absolute;left:2830;top:11680;"> <v:oval id="_x0000_s1040" style="'position:absolute;left:7525;top:11680;"> <v:oval id="_x0000_s1041" style="'position:absolute;left:7682;top:11840;"> <v:line id="_x0000_s1042" style="'position:absolute'" from="4238,12160" to="7525,12160"> <v:line id="_x0000_s1043" style="'position:absolute'" from="4238,12480" to="7525,12480"> <v:shapetype id="_x0000_t202" coordsize="21600,21600" spt="202" path="m,l,21600r21600,l21600,xe"> <v:stroke joinstyle="miter"> <v:path gradientshapeok="t" connecttype="rect"> </v:shapetype><v:shape id="_x0000_s1044" type="#_x0000_t202" style="'position:absolute;"> <v:textbox style="'mso-next-textbox:#_x0000_s1044'"> <![if !mso]> <table cellpadding="0" cellspacing="0" width="100%"> <tr> <td><![endif]> <div> <p class="MsoNormal"><span style="'mso-ansi-language:EN-US'">Rounded Connecting Rod rodrod<o:p></o:p></span></p> </div> <![if !mso]></td> </tr> </table> <![endif]></v:textbox> </v:shape><v:shape id="_x0000_s1045" type="#_x0000_t202" style="'position:absolute;"> <v:textbox style="'mso-next-textbox:#_x0000_s1045'"> <![if !mso]> <table cellpadding="0" cellspacing="0" width="100%"> <tr> <td><![endif]> <div> <p class="MsoNormal"><span style="'mso-ansi-language:EN-US'"><span style="'mso-spacerun:yes'"> </span>Rectangular Connecting Rod<o:p></o:p></span></p> </div> <![if !mso]></td> </tr> </table> <![endif]></v:textbox> </v:shape><v:shape id="_x0000_s1046" type="#_x0000_t202" style="'position:absolute;"> <v:textbox style="'mso-next-textbox:#_x0000_s1046'"> <![if !mso]> <table cellpadding="0" cellspacing="0" width="100%"> <tr> <td><![endif]> <div> <p class="MsoNormal"><span style="'font-size:9.0pt;mso-ansi-language:EN-US'">104.45gm<o:p></o:p></span></p> </div> <![if !mso]></td> </tr> </table> <![endif]></v:textbox> </v:shape><v:shape id="_x0000_s1047" type="#_x0000_t202" style="'position:absolute;"> <v:textbox style="'mso-next-textbox:#_x0000_s1047'"> <![if !mso]> <table cellpadding="0" cellspacing="0" width="100%"> <tr> <td><![endif]> <div> <p class="MsoNormal"><span style="'font-size:9.0pt;mso-ansi-language:EN-US'">48gm<o:p></o:p></span></p> </div> <![if !mso]></td> </tr> </table> <![endif]></v:textbox> </v:shape><v:shape id="_x0000_s1048" type="#_x0000_t202" style="'position:absolute;"> <v:textbox style="'mso-next-textbox:#_x0000_s1048'"> <![if !mso]> <table cellpadding="0" cellspacing="0" width="100%"> <tr> <td><![endif]> <div> <p class="MsoNormal"><span style="'mso-ansi-language:EN-US'"><span style="'mso-spacerun:yes'"> </span>160.95gm<o:p></o:p></span></p> </div> <![if !mso]></td> </tr> </table> <![endif]></v:textbox> </v:shape><v:shape id="_x0000_s1049" type="#_x0000_t202" style="'position:absolute;"> <v:textbox style="'mso-next-textbox:#_x0000_s1049'"> <![if !mso]> <table cellpadding="0" cellspacing="0" width="100%"> <tr> <td><![endif]> <div> <p class="MsoNormal"><span style="'mso-ansi-language:EN-US'"><span style="'mso-spacerun:yes'"> </span>94.35gm<o:p></o:p></span></p> </div> <![if !mso]></td> </tr> </table> <![endif]></v:textbox> </v:shape><v:shape id="_x0000_s1050" type="#_x0000_t202" style="'position:absolute;"> <v:textbox style="'mso-next-textbox:#_x0000_s1050'"> <![if !mso]> <table cellpadding="0" cellspacing="0" width="100%"> <tr> <td><![endif]> <div> <p class="MsoNormal"><span style="'font-size:9.0pt;mso-ansi-language:EN-US'">100.55gmgm<o:p></o:p></span></p> </div> <![if !mso]></td> </tr> </table> <![endif]></v:textbox> </v:shape><v:shape id="_x0000_s1051" type="#_x0000_t202" style="'position:absolute;"> <v:textbox style="'mso-next-textbox:#_x0000_s1051'"> <![if !mso]> <table cellpadding="0" cellspacing="0" width="100%"> <tr> <td><![endif]> <div> <p class="MsoNormal"><span style="'font-size:9.0pt;mso-ansi-language:EN-US'"><span style="'mso-spacerun:yes'"> </span>44.1gm<o:p></o:p></span></p> </div> <![if !mso]></td> </tr> </table> <![endif]></v:textbox> </v:shape><w:wrap type="none"> <w:anchorlock/> </v:group><![endif]--><img width="552" height="372" src="file:///C:/DOCUME~1/d8/LOCALS~1/Temp/msohtml1/01/clip_image001.gif" shapes="_x0000_s1026 _x0000_s1027 _x0000_s1028 _x0000_s1029 _x0000_s1030 _x0000_s1031 _x0000_s1032 _x0000_s1033 _x0000_s1034 _x0000_s1035 _x0000_s1036 _x0000_s1037 _x0000_s1038 _x0000_s1039 _x0000_s1040 _x0000_s1041 _x0000_s1042 _x0000_s1043 _x0000_s1044 _x0000_s1045 _x0000_s1046 _x0000_s1047 _x0000_s1048 _x0000_s1049 _x0000_s1050 _x0000_s1051" /></span><!--[if mso & !supportInlineShapes & supportFields]><span lang="EN-GB"><v:shape id="_x0000_i1025" type="#_x0000_t75" style="'width:414pt;"> <v:imagedata croptop="-65520f" cropbottom="65520f"> </v:shape><span style="'mso-element:field-end'"></span></span><![endif]--></p> <p class="MsoNormal" style="line-height:150%;tab-stops:1.0in 81.0pt"><span lang="EN-GB"><o:p> </o:p></span></p> <p class="MsoNormal" style="line-height:150%;tab-stops:1.0in 81.0pt"><!--[if gte vml 1]><v:shape id="_x0000_s1076" type="#_x0000_t202" style="'position:absolute;margin-left:81pt;"> <v:textbox style="'mso-next-textbox:#_x0000_s1076'/"> </v:shape><![endif]--><span style="mso-ignore:vglayout;position: relative;z-index:3"><span style="position:absolute;left:107px;top:-25px; width:66px;height:30px"> <table cellpadding="0" cellspacing="0"> <tbody><tr> <td width="66" height="30" bgcolor="white" style="border:.75pt solid black; vertical-align:top;background:white"><span style="position:absolute;mso-ignore:vglayout;z-index:3"> <table cellpadding="0" cellspacing="0" width="100%"> <tbody><tr> <td> <div shape="_x0000_s1076" style="padding:4.35pt 7.95pt 4.35pt 7.95pt" class="shape"> <p class="MsoNormal"><span style="font-size:9.0pt;mso-ansi-language:EN-US">40mm<o:p></o:p></span></p> </div> </td> </tr> </tbody></table> </span> </td> </tr> </tbody></table> </span></span><!--[if mso & !supportInlineShapes & supportFields]><span lang="EN-GB"><span style="'mso-element:field-begin;mso-field-lock:yes'"></span><span style="'mso-spacerun:yes'"> </span>SHAPE<span style="'mso-spacerun:yes'"> </span>\* MERGEFORMAT <span style="'mso-element:field-separator'"></span></span><![endif]--><span lang="EN-GB"><!--[if gte vml 1]><v:group id="_x0000_s1052" editas="canvas" style="'width:414pt;height:297pt;mso-position-horizontal-relative:char;" coordorigin="2360,1830" coordsize="7200,5280"> <o:lock ext="edit" aspectratio="t"> <v:shape id="_x0000_s1053" type="#_x0000_t75" style="'position:absolute;left:2360;" preferrelative="f"> <v:fill detectmouseclick="t"> <v:path extrusionok="t" connecttype="none"> <o:lock ext="edit" text="t"> </v:shape><v:line id="_x0000_s1054" style="'position:absolute'" from="3299,2150" to="5177,2150"> <v:line id="_x0000_s1055" style="'position:absolute;flip:x'" from="2517,2150" to="3299,5990"> <v:line id="_x0000_s1056" style="'position:absolute'" from="2517,5990" to="5647,5990"> <v:line id="_x0000_s1057" style="'position:absolute'" from="5177,2150" to="5960,5990"> <v:line id="_x0000_s1058" style="'position:absolute'" from="5334,5990" to="5960,5990"> <v:oval id="_x0000_s1059" style="'position:absolute;left:4082;top:2630;width:313;"> <v:oval id="_x0000_s1060" style="'position:absolute;left:4082;top:5030;width:312;"> <v:line id="_x0000_s1061" style="'position:absolute'" from="4238,5510" to="4238,5990"> <v:stroke endarrow="block"> </v:line><v:line id="_x0000_s1062" style="'position:absolute;flip:y'" from="4238,5350" to="4238,5830"> <v:stroke endarrow="block"> </v:line><v:line id="_x0000_s1063" style="'position:absolute;flip:y'" from="4238,2950" to="4238,4870"> <v:stroke endarrow="block"> </v:line><v:line id="_x0000_s1064" style="'position:absolute'" from="4238,4390" to="4238,5030"> <v:stroke endarrow="block"> </v:line><v:line id="_x0000_s1065" style="'position:absolute;flip:y'" from="4238,2150" to="4238,2470"> <v:stroke endarrow="block"> </v:line><v:line id="_x0000_s1066" style="'position:absolute'" from="4238,2310" to="4238,2630"> <v:stroke endarrow="block"> </v:line><v:line id="_x0000_s1067" style="'position:absolute'" from="3456,1990" to="5177,1990"> <v:stroke endarrow="block"> </v:line><v:line id="_x0000_s1068" style="'position:absolute;flip:x'" from="3299,1990" to="3925,1990"> <v:stroke endarrow="block"> </v:line><v:line id="_x0000_s1069" style="'position:absolute'" from="3769,6150" to="5960,6150"> <v:stroke endarrow="block"> </v:line><v:line id="_x0000_s1070" style="'position:absolute;flip:x'" from="2517,6150" to="4082,6150"> <v:stroke endarrow="block"> </v:line><v:shape id="_x0000_s1071" type="#_x0000_t202" style="'position:absolute;"> <v:textbox style="'mso-next-textbox:#_x0000_s1071'"> <![if !mso]> <table cellpadding="0" cellspacing="0" width="100%"> <tr> <td><![endif]> <div> <p class="MsoNormal"><span style="'font-size:9.0pt;mso-ansi-language:EN-US'">9.25mm<o:p></o:p></span></p> </div> <![if !mso]></td> </tr> </table> <![endif]></v:textbox> </v:shape><v:shape id="_x0000_s1072" type="#_x0000_t202" style="'position:absolute;"> <v:textbox style="'mso-next-textbox:#_x0000_s1072'"> <![if !mso]> <table cellpadding="0" cellspacing="0" width="100%"> <tr> <td><![endif]> <div> <p class="MsoNormal"><span style="'font-size:9.0pt;mso-ansi-language:EN-US'">9.6mm<o:p></o:p></span></p> </div> <![if !mso]></td> </tr> </table> <![endif]></v:textbox> </v:shape><v:shape id="_x0000_s1073" type="#_x0000_t202" style="'position:absolute;"> <v:textbox style="'mso-next-textbox:#_x0000_s1073'"> <![if !mso]> <table cellpadding="0" cellspacing="0" width="100%"> <tr> <td><![endif]> <div> <p class="MsoNormal"><span style="'font-size:9.0pt;mso-ansi-language:EN-US'">274.7mm<o:p></o:p></span></p> <p class="MsoNormal"><span style="'mso-ansi-language:EN-US'">7<o:p></o:p></span></p> </div> <![if !mso]></td> </tr> </table> <![endif]></v:textbox> </v:shape><v:shape id="_x0000_s1074" type="#_x0000_t202" style="'position:absolute;"> <v:textbox style="'mso-next-textbox:#_x0000_s1074'"> <![if !mso]> <table cellpadding="0" cellspacing="0" width="100%"> <tr> <td><![endif]> <div> <p class="MsoNormal"><span style="'font-size:9.0pt;mso-ansi-language:EN-US'">143mm<o:p></o:p></span></p> </div> <![if !mso]></td> </tr> </table> <![endif]></v:textbox> </v:shape><v:shape id="_x0000_s1075" type="#_x0000_t202" style="'position:absolute;"> <v:textbox> <![if !mso]> <table cellpadding="0" cellspacing="0" width="100%"> <tr> <td><![endif]> <div> <p class="MsoNormal"><span style="'font-size:9.0pt;mso-ansi-language:EN-US'"><span style="'mso-spacerun:yes'"> </span>352.9gm<o:p></o:p></span></p> </div> <![if !mso]></td> </tr> </table> <![endif]></v:textbox> </v:shape><w:wrap type="none"> <w:anchorlock/> </v:group><![endif]--><img width="552" height="399" src="file:///C:/DOCUME~1/d8/LOCALS~1/Temp/msohtml1/01/clip_image002.gif" shapes="_x0000_s1052 _x0000_s1053 _x0000_s1054 _x0000_s1055 _x0000_s1056 _x0000_s1057 _x0000_s1058 _x0000_s1059 _x0000_s1060 _x0000_s1061 _x0000_s1062 _x0000_s1063 _x0000_s1064 _x0000_s1065 _x0000_s1066 _x0000_s1067 _x0000_s1068 _x0000_s1069 _x0000_s1070 _x0000_s1071 _x0000_s1072 _x0000_s1073 _x0000_s1074 _x0000_s1075" /></span><!--[if mso & !supportInlineShapes & supportFields]><span lang="EN-GB"><v:shape id="_x0000_i1026" type="#_x0000_t75" style="'width:414pt;"> <v:imagedata croptop="-65520f" cropbottom="65520f"> </v:shape><span style="'mso-element:field-end'"></span></span><![endif]--></p> <p class="MsoNormal" style="line-height:150%;tab-stops:1.0in 81.0pt"><span lang="EN-GB"><o:p> </o:p></span></p> <p class="MsoNormal" style="line-height:150%;tab-stops:1.0in 81.0pt"><span lang="EN-GB"><o:p> </o:p></span></p> <p class="MsoNormal" style="line-height:150%;tab-stops:1.0in 81.0pt"><span lang="EN-GB">When the connecting rod is suspended at A, the periodic time is given by:- </span></p> <p class="MsoNormal" style="line-height:150%;tab-stops:1.0in 81.0pt"><span lang="EN-GB"><o:p> </o:p></span></p> <p class="MsoNormal" style="line-height:150%;tab-stops:1.0in 81.0pt"><span lang="EN-GB"><span style="position:relative;top:16.0pt;mso-text-raise:-16.0pt"><!--[if gte vml 1]><v:shape id="_x0000_i1029" type="#_x0000_t75" style="'width:93pt;height:39.75pt'" ole=""> <v:imagedata src="file:///C:\DOCUME~1\d8\LOCALS~1\Temp\msohtml1\01\clip_image003.wmz" title=""> </v:shape><![endif]--><img width="124" height="53" src="file:///C:/DOCUME~1/d8/LOCALS~1/Temp/msohtml1/01/clip_image004.gif" shapes="_x0000_i1029" /></span><!--[if gte mso 9]><xml> <o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1029" drawaspect="Content" objectid="_1293705975"> </o:OLEObject> </xml><![endif]--><span style="mso-tab-count:2"> </span>(i)</span></p> <p class="MsoNormal" style="line-height:150%;tab-stops:1.0in 81.0pt"><span lang="EN-GB"><o:p> </o:p></span></p> <p class="MsoNormal" style="line-height:150%;tab-stops:1.0in 81.0pt"><span lang="EN-GB">When the conrod is suspended at B, the periodic time is given by:-</span></p> <p class="MsoNormal" style="line-height:150%;tab-stops:1.0in 81.0pt"><span lang="EN-GB"><o:p> </o:p></span></p> <p class="MsoNormal" style="line-height:150%;tab-stops:1.0in 81.0pt"><span lang="EN-GB"><span style="position:relative;top:16.0pt;mso-text-raise:-16.0pt"><!--[if gte vml 1]><v:shape id="_x0000_i1030" type="#_x0000_t75" style="'width:92.25pt;height:39pt'" ole=""> <v:imagedata src="file:///C:\DOCUME~1\d8\LOCALS~1\Temp\msohtml1\01\clip_image005.wmz" title=""> </v:shape><![endif]--><img width="123" height="52" src="file:///C:/DOCUME~1/d8/LOCALS~1/Temp/msohtml1/01/clip_image006.gif" shapes="_x0000_i1030" /></span><!--[if gte mso 9]><xml> <o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1030" drawaspect="Content" objectid="_1293705976"> </o:OLEObject> </xml><![endif]--><span style="mso-tab-count:2"> </span>(ii)</span></p> <p class="MsoNormal" style="line-height:150%;tab-stops:1.0in 81.0pt"><span lang="EN-GB"><o:p> </o:p></span></p> <p class="MsoNormal" style="line-height:150%;tab-stops:1.0in 81.0pt"><span lang="EN-GB">At the same,total length between A and B is:-</span></p> <p class="MsoNormal" style="line-height:150%;tab-stops:1.0in 81.0pt"><span lang="EN-GB"><o:p> </o:p></span></p> <p class="MsoNormal" style="line-height:150%;tab-stops:1.0in 81.0pt"><span lang="EN-GB"><span style="position:relative;top:5.0pt;mso-text-raise:-5.0pt"><!--[if gte vml 1]><v:shape id="_x0000_i1031" type="#_x0000_t75" style="'width:65.25pt;height:17.25pt'" ole=""> <v:imagedata src="file:///C:\DOCUME~1\d8\LOCALS~1\Temp\msohtml1\01\clip_image007.wmz" title=""> </v:shape><![endif]--><img width="87" height="23" src="file:///C:/DOCUME~1/d8/LOCALS~1/Temp/msohtml1/01/clip_image008.gif" shapes="_x0000_i1031" /></span><!--[if gte mso 9]><xml> <o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1031" drawaspect="Content" objectid="_1293705977"> </o:OLEObject> </xml><![endif]--><span style="mso-tab-count:4"> </span>(iii)</span></p> <p class="MsoNormal" style="line-height:150%;tab-stops:1.0in 81.0pt"><span lang="EN-GB"><o:p> </o:p></span></p> <p class="MsoNormal" style="line-height:150%;tab-stops:1.0in 81.0pt"><span lang="EN-GB"><o:p> </o:p></span></p> <p class="MsoNormal" style="line-height:150%;tab-stops:1.0in 81.0pt"><span lang="EN-GB"><o:p> </o:p></span></p> <p class="MsoNormal" style="line-height:150%;tab-stops:1.0in 81.0pt"><span lang="EN-GB">It can be seen that in equation (i),(ii) and (iii) there are three unknowns, i.e. k, <span style="position:relative;top:5.0pt;mso-text-raise:-5.0pt"><!--[if gte vml 1]><v:shape id="_x0000_i1027" type="#_x0000_t75" style="'width:15pt;height:17.25pt'" ole=""> <v:imagedata src="file:///C:\DOCUME~1\d8\LOCALS~1\Temp\msohtml1\01\clip_image009.wmz" title=""> </v:shape><![endif]--><img width="20" height="23" src="file:///C:/DOCUME~1/d8/LOCALS~1/Temp/msohtml1/01/clip_image010.gif" shapes="_x0000_i1027" /></span><!--[if gte mso 9]><xml> <o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1027" drawaspect="Content" objectid="_1293705978"> </o:OLEObject> </xml><![endif]--><span style="mso-spacerun:yes"> </span>and <span style="position:relative;top:5.0pt;mso-text-raise:-5.0pt"><!--[if gte vml 1]><v:shape id="_x0000_i1028" type="#_x0000_t75" style="'width:15pt;height:17.25pt'" ole=""> <v:imagedata src="file:///C:\DOCUME~1\d8\LOCALS~1\Temp\msohtml1\01\clip_image011.wmz" title=""> </v:shape><![endif]--><img width="20" height="23" src="file:///C:/DOCUME~1/d8/LOCALS~1/Temp/msohtml1/01/clip_image012.gif" shapes="_x0000_i1028" /></span><!--[if gte mso 9]><xml> <o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1028" drawaspect="Content" objectid="_1293705979"> </o:OLEObject> </xml><![endif]-->.Therefore, solving the three equations simultaneously, the three unknowns can be determined.</span></p>d8http://www.blogger.com/profile/09390427562617157781noreply@blogger.com0tag:blogger.com,1999:blog-6305446887053345257.post-60615349937449509592009-01-05T19:14:00.000-08:002009-01-16T21:54:46.349-08:00Method<p class="MsoNormal" style="line-height:150%;tab-stops:1.0in 81.0pt"><br /></p> <ol style="margin-top:0in" start="1" type="1"> <li class="MsoNormal" style="line-height:150%;mso-list:l0 level1 lfo1; tab-stops:list .5in left 1.0in 81.0pt"><span lang="EN-GB">First of all, a rounded connecting rod is placed at the hinge with the smaller radius of circle at the top and the larger radius of circle at the bottom. </span></li> <li class="MsoNormal" style="line-height:150%;mso-list:l0 level1 lfo1; tab-stops:list .5in left 1.0in 81.0pt"><span lang="EN-GB">Then, the rod is set at an angle of<span style="position:relative;top:3.0pt;mso-text-raise: -3.0pt"><!--[if gte vml 1]><v:shapetype id="_x0000_t75" coordsize="21600,21600" spt="75" preferrelative="t" path="m@4@5l@4@11@9@11@9@5xe" filled="f" stroked="f"> <v:stroke joinstyle="miter"> <v:formulas> <v:f eqn="if lineDrawn pixelLineWidth 0"> <v:f eqn="sum @0 1 0"> <v:f eqn="sum 0 0 @1"> <v:f eqn="prod @2 1 2"> <v:f eqn="prod @3 21600 pixelWidth"> <v:f eqn="prod @3 21600 pixelHeight"> <v:f eqn="sum @0 0 1"> <v:f eqn="prod @6 1 2"> <v:f eqn="prod @7 21600 pixelWidth"> <v:f eqn="sum @8 21600 0"> <v:f eqn="prod @7 21600 pixelHeight"> <v:f eqn="sum @10 21600 0"> </v:formulas> <v:path extrusionok="f" gradientshapeok="t" connecttype="rect"> <o:lock ext="edit" aspectratio="t"> </v:shapetype><v:shape id="_x0000_i1025" type="#_x0000_t75" style="'width:18pt;" ole=""> <v:imagedata src="file:///C:\DOCUME~1\d8\LOCALS~1\Temp\msohtml1\01\clip_image001.wmz" title=""> </v:shape><![endif]--><img width="24" height="21" src="file:///C:/DOCUME~1/d8/LOCALS~1/Temp/msohtml1/01/clip_image002.gif" shapes="_x0000_i1025" /></span><!--[if gte mso 9]><xml> <o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1025" drawaspect="Content" objectid="_1293705890"> </o:OLEObject> </xml><![endif]-->. Next, release the rod and at the same moment time is taken for ten swings. This action is repeated at the opposite side and the average reading for ten swings is then calculated.</span></li> <li class="MsoNormal" style="line-height:150%;mso-list:l0 level1 lfo1; tab-stops:list .5in left 1.0in 81.0pt"><span lang="EN-GB">Later, the rounded connecting rod is turned upside down with the larger radius of circle at the hinge and the same steps as above are repeated.</span></li> <li class="MsoNormal" style="line-height:150%;mso-list:l0 level1 lfo1; tab-stops:list .5in left 1.0in 81.0pt"><span lang="EN-GB">After the first experiment has been done, the steps are repeated by using rectangular connecting rod and also prismatic thick plane. </span></li> </ol> <p class="MsoNormal" style="line-height:150%;tab-stops:1.0in 81.0pt"><span lang="EN-GB"><o:p> </o:p></span></p>d8http://www.blogger.com/profile/09390427562617157781noreply@blogger.com0tag:blogger.com,1999:blog-6305446887053345257.post-77552658532686407022009-01-04T14:23:00.000-08:002009-01-16T21:54:05.093-08:00APPARATUS<p class="MsoNormal"><span class="Apple-style-span" style="font-weight: bold;"><br /></span></p> <p class="MsoNormal"><span lang="EN-GB"><o:p> </o:p></span></p> <p class="MsoNormal"><!--[if gte vml 1]><v:rect id="_x0000_s1028" style="'position:absolute;" filled="f" stroked="f"> <v:textbox style="'mso-next-textbox:#_x0000_s1028'/"> </v:rect><![endif]--><span style="mso-ignore:vglayout;position: absolute;z-index:3;margin-left:0px;margin-top:7px;width:47px;height:44px"> <table cellpadding="0" cellspacing="0"> <tbody><tr> <td width="47" height="44" style="vertical-align:top"><span style="position:absolute;mso-ignore:vglayout;z-index:3"> <table cellpadding="0" cellspacing="0" width="100%"> <tbody><tr> <td> <div shape="_x0000_s1028" style="padding:3.6pt 7.2pt 3.6pt 7.2pt" class="shape"> <p class="MsoNormal"><b style="mso-bidi-font-weight:normal"><span lang="EN-GB" style="font-family:Arial">1<o:p></o:p></span></b></p> </div> </td> </tr> </tbody></table> </span> </td> </tr> </tbody></table> </span><!--[if gte vml 1]><v:rect id="_x0000_s1027" style="'position:absolute;" filled="f" stroked="f"> <v:textbox style="'mso-next-textbox:#_x0000_s1027'/"> </v:rect><![endif]--><span style="mso-ignore:vglayout;position: absolute;z-index:2;margin-left:211px;margin-top:7px;width:46px;height:44px"> <table cellpadding="0" cellspacing="0"> <tbody><tr> <td width="46" height="44" style="vertical-align:top"><span style="position:absolute;mso-ignore:vglayout;z-index:2"> <table cellpadding="0" cellspacing="0" width="100%"> <tbody><tr> <td> <div shape="_x0000_s1027" style="padding:3.6pt 7.2pt 3.6pt 7.2pt" class="shape"> <p class="MsoNormal"><b style="mso-bidi-font-weight:normal"><span lang="EN-GB" style="font-family:Arial">2<o:p></o:p></span></b></p> </div> </td> </tr> </tbody></table> </span> </td> </tr> </tbody></table> </span><!--[if gte vml 1]><v:rect id="_x0000_s1026" style="'position:absolute;" filled="f" stroked="f"> <v:textbox style="'mso-next-textbox:#_x0000_s1026'/"> </v:rect><![endif]--><span style="mso-ignore:vglayout;position: absolute;z-index:1;margin-left:429px;margin-top:7px;width:47px;height:44px"> <table cellpadding="0" cellspacing="0"> <tbody><tr> <td width="47" height="44" style="vertical-align:top"><span style="position:absolute;mso-ignore:vglayout;z-index:1"> <table cellpadding="0" cellspacing="0" width="100%"> <tbody><tr> <td> <div shape="_x0000_s1026" style="padding:3.6pt 7.2pt 3.6pt 7.2pt" class="shape"> <p class="MsoNormal"><b style="mso-bidi-font-weight:normal"><span lang="EN-GB" style="font-family:Arial">3<o:p></o:p></span></b></p> </div> </td> </tr> </tbody></table> </span> </td> </tr> </tbody></table> </span><span lang="EN-GB"><!--[if gte vml 1]><v:shapetype id="_x0000_t75" coordsize="21600,21600" spt="75" preferrelative="t" path="m@4@5l@4@11@9@11@9@5xe" filled="f" stroked="f"> <v:stroke joinstyle="miter"> <v:formulas> <v:f eqn="if lineDrawn pixelLineWidth 0"> <v:f eqn="sum @0 1 0"> <v:f eqn="sum 0 0 @1"> <v:f eqn="prod @2 1 2"> <v:f eqn="prod @3 21600 pixelWidth"> <v:f eqn="prod @3 21600 pixelHeight"> <v:f eqn="sum @0 0 1"> <v:f eqn="prod @6 1 2"> <v:f eqn="prod @7 21600 pixelWidth"> <v:f eqn="sum @8 21600 0"> <v:f eqn="prod @7 21600 pixelHeight"> <v:f eqn="sum @10 21600 0"> </v:formulas> <v:path extrusionok="f" gradientshapeok="t" connecttype="rect"> <o:lock ext="edit" aspectratio="t"> </v:shapetype><v:shape id="_x0000_i1025" type="#_x0000_t75" style="'width:104.25pt;" ole=""> <v:imagedata src="file:///C:\DOCUME~1\d8\LOCALS~1\Temp\msohtml1\01\clip_image001.png" title="" gain="41943f"> </v:shape><![endif]--><img width="139" height="450" src="file:///C:/DOCUME~1/d8/LOCALS~1/Temp/msohtml1/01/clip_image002.jpg" shapes="_x0000_i1025" /><!--[if gte mso 9]><xml> <o:oleobject type="Embed" progid="MSPhotoEd.3" shapeid="_x0000_i1025" drawaspect="Content" objectid="_1293705848"> </o:OLEObject> </xml><![endif]--><span style="mso-spacerun:yes"> </span><!--[if gte vml 1]><v:shape id="_x0000_i1026" type="#_x0000_t75" style="'width:102pt;height:333.75pt'" ole=""> <v:imagedata src="file:///C:\DOCUME~1\d8\LOCALS~1\Temp\msohtml1\01\clip_image003.png" title="" gain="41943f"> </v:shape><![endif]--><img width="136" height="445" src="file:///C:/DOCUME~1/d8/LOCALS~1/Temp/msohtml1/01/clip_image004.jpg" shapes="_x0000_i1026" /><!--[if gte mso 9]><xml> <o:oleobject type="Embed" progid="MSPhotoEd.3" shapeid="_x0000_i1026" drawaspect="Content" objectid="_1293705850"> </o:OLEObject> </xml><![endif]--><span style="mso-spacerun:yes"> </span><!--[if gte vml 1]><v:shape id="_x0000_i1027" type="#_x0000_t75" style="'width:129.75pt;height:333.75pt'" ole=""> <v:imagedata src="file:///C:\DOCUME~1\d8\LOCALS~1\Temp\msohtml1\01\clip_image005.png" title="" gain="79922f"> </v:shape><![endif]--><img width="173" height="445" src="file:///C:/DOCUME~1/d8/LOCALS~1/Temp/msohtml1/01/clip_image006.jpg" shapes="_x0000_i1027" /><!--[if gte mso 9]><xml> <o:oleobject type="Embed" progid="MSPhotoEd.3" shapeid="_x0000_i1027" drawaspect="Content" objectid="_1293705851"> </o:OLEObject> </xml><![endif]--></span></p> <p class="MsoNormal"><sub><span lang="EN-GB" style="font-size:11.0pt;mso-bidi-font-size: 12.0pt"><span style="mso-spacerun:yes"> </span></span></sub></p> <ol style="margin-top:0in" start="1" type="1"> <li class="MsoNormal" style="mso-list:l0 level1 lfo1;tab-stops:list .5in"><span lang="EN-GB">Connecting Bar</span></li> </ol> <p class="MsoNormal" style="margin-left:35.4pt"><span lang="EN-GB">Total length: 290mm</span></p> <p class="MsoNormal" style="margin-left:35.4pt"><span lang="EN-GB"><o:p> </o:p></span></p> <ol style="margin-top:0in" start="2" type="1"> <li class="MsoNormal" style="mso-list:l0 level1 lfo1;tab-stops:list .5in"><span lang="EN-GB">Connecting Rod</span></li> </ol> <p class="MsoNormal" style="margin-left:35.4pt"><span lang="EN-GB">Total length: 291mm</span></p> <p class="MsoNormal" style="margin-left:35.4pt"><span lang="EN-GB"><o:p> </o:p></span></p> <ol style="margin-top:0in" start="3" type="1"> <li class="MsoNormal" style="mso-list:l0 level1 lfo1;tab-stops:list .5in"><span lang="EN-GB">Triangle</span></li> </ol> <p class="MsoNormal" style="margin-left:35.4pt"><span lang="EN-GB">Total length: 293.55mm</span></p> <p class="MsoNormal" style="margin-left:35.4pt"><span lang="EN-GB"><o:p> </o:p></span></p> <ol style="margin-top:0in" start="4" type="1"> <li class="MsoNormal" style="mso-list:l0 level1 lfo1;tab-stops:list .5in"><span lang="EN-GB">Stopwatch</span></li></ol>d8http://www.blogger.com/profile/09390427562617157781noreply@blogger.com0tag:blogger.com,1999:blog-6305446887053345257.post-70685568125426174232009-01-03T21:50:00.000-08:002009-01-16T21:53:23.031-08:00Objective<p class="MsoNormal" style="line-height:150%"><br /></p> <p class="MsoNormal" style="line-height:150%"><span style="mso-ansi-language: EN-US"><span style="mso-tab-count:1"> </span>: To determine the centre of gravity of a connecting rod, as well as the <o:p></o:p></span></p> <p class="MsoNormal" style="line-height:150%"><span style="mso-ansi-language: EN-US"><span style="mso-tab-count:2"> </span><span style="mso-spacerun:yes"> </span>Radius of gyration about the centre of gravity.<o:p></o:p></span></p> <p class="MsoNormal" style="line-height:150%"><span style="mso-ansi-language: EN-US">Theory<span style="mso-tab-count:2"> </span></span></p><p class="MsoNormal" style="line-height:150%"><span style="mso-ansi-language: EN-US"><span style="mso-tab-count:2"></span>:<span style="mso-spacerun:yes"> </span>Moment at O:<o:p></o:p></span></p> <p class="MsoNormal"><span lang="EN-GB" style="font-family:Arial"><o:p> </o:p></span></p> <p class="MsoNormal"><!--[if mso & !supportInlineShapes & supportFields]><span lang="EN-GB"><span style="'mso-element:field-begin;mso-field-lock:yes'"></span><span style="'mso-spacerun:yes'"> </span>SHAPE<span style="'mso-spacerun:yes'"> </span>\* MERGEFORMAT <span style="'mso-element:field-separator'"></span></span><![endif]--><span lang="EN-GB"><!--[if gte vml 1]><v:group id="_x0000_s1054" editas="canvas" style="'width:608pt;height:347.1pt;mso-position-horizontal-relative:char;" coordorigin="5263,2850" coordsize="6047,3452"> <o:lock ext="edit" aspectratio="t"> <v:shapetype id="_x0000_t75" coordsize="21600,21600" spt="75" preferrelative="t" path="m@4@5l@4@11@9@11@9@5xe" filled="f" stroked="f"> <v:stroke joinstyle="miter"> <v:formulas> <v:f eqn="if lineDrawn pixelLineWidth 0"> <v:f eqn="sum @0 1 0"> <v:f eqn="sum 0 0 @1"> <v:f eqn="prod @2 1 2"> <v:f eqn="prod @3 21600 pixelWidth"> <v:f eqn="prod @3 21600 pixelHeight"> <v:f eqn="sum @0 0 1"> <v:f eqn="prod @6 1 2"> <v:f eqn="prod @7 21600 pixelWidth"> <v:f eqn="sum @8 21600 0"> <v:f eqn="prod @7 21600 pixelHeight"> <v:f eqn="sum 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lang="EN-GB" style="'font-family:Arial'">O <o:p></o:p></span></p> </div> <![if !mso]></td> </tr> </table> <![endif]></v:textbox> </v:rect><v:rect id="_x0000_s1061" style="'position:absolute;left:8065;top:4858;" filled="f" stroked="f"> <v:textbox style="'mso-next-textbox:#_x0000_s1061'"> <![if !mso]> <table cellpadding="0" cellspacing="0" width="100%"> <tr> <td><![endif]> <div> <p class="MsoNormal"><span lang="EN-GB" style="'font-family:Arial'">G<o:p></o:p></span></p> </div> <![if !mso]></td> </tr> </table> <![endif]></v:textbox> </v:rect><v:shapetype id="_x0000_t19" coordsize="21600,21600" spt="19" adj="-5898240,,,21600,21600" path="wr-21600,,21600,43200,,,21600,21600nfewr-21600,,21600,43200,,,21600,21600l,21600nsxe" filled="f"> <v:formulas> <v:f eqn="val #2"> <v:f eqn="val #3"> <v:f eqn="val #4"> </v:formulas> <v:path arrowok="t" extrusionok="f" gradientshapeok="t" connecttype="custom" connectlocs="0,0;21600,21600;0,21600"> <v:handles> <v:h position="@2,#0" polar="@0,@1"> <v:h position="@2,#1" polar="@0,@1"> </v:handles> </v:shapetype><v:shape id="_x0000_s1062" type="#_x0000_t19" style="'position:absolute;" coordsize="7664,21600" adj=",-4536348" path="wr-21600,,21600,43200,,,7664,1405nfewr-21600,,21600,43200,,,7664,1405l,21600nsxe"> <v:path connectlocs="0,0;7664,1405;0,21600"> </v:shape><v:rect id="_x0000_s1063" style="'position:absolute;left:7350;top:4625;" filled="f" stroked="f"> <v:textbox style="'mso-next-textbox:#_x0000_s1063'"> <![if !mso]> <table cellpadding="0" cellspacing="0" width="100%"> <tr> <td><![endif]> <div> <p class="MsoNormal"><span lang="EN-GB" style="'font-family:Arial'">θ</span></p> </div> <![if !mso]></td> </tr> </table> <![endif]></v:textbox> </v:rect><w:wrap type="none"> <w:anchorlock/> </v:group><![endif]--><img width="811" height="463" src="file:///C:/DOCUME~1/d8/LOCALS~1/Temp/msohtml1/01/clip_image001.gif" shapes="_x0000_s1054 _x0000_s1055 _x0000_s1056 _x0000_s1057 _x0000_s1058 _x0000_s1059 _x0000_s1060 _x0000_s1061 _x0000_s1062 _x0000_s1063" /></span><!--[if mso & !supportInlineShapes & supportFields]><span lang="EN-GB"><v:shape id="_x0000_i1025" type="#_x0000_t75" style="'width:608pt;"> <v:imagedata croptop="-65520f" cropbottom="65520f"> </v:shape><span style="'mso-element:field-end'"></span></span><![endif]--></p> <p class="MsoNormal"><span lang="EN-GB"><o:p> </o:p></span></p> <p class="MsoNormal"><span lang="EN-GB"><o:p> </o:p></span></p> <p class="MsoNormal"><span lang="EN-GB"><o:p> </o:p></span></p> <p class="MsoNormal"><span lang="EN-GB"><o:p> </o:p></span></p> <p class="MsoNormal" style="margin-left:2.0in;text-indent:.5in;line-height:150%"><span style="mso-ansi-language:EN-US"><span style="position:relative;top:6.0pt; mso-text-raise:-6.0pt"><!--[if gte vml 1]><v:shape id="_x0000_i1027" type="#_x0000_t75" style="'width:99pt;height:18pt'" ole=""> <v:imagedata src="file:///C:\DOCUME~1\d8\LOCALS~1\Temp\msohtml1\01\clip_image002.wmz" title=""> </v:shape><![endif]--><img width="132" height="24" src="file:///C:/DOCUME~1/d8/LOCALS~1/Temp/msohtml1/01/clip_image003.gif" shapes="_x0000_i1027" /></span><!--[if gte mso 9]><xml> <o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1027" drawaspect="Content" objectid="_1293705748"> </o:OLEObject> </xml><![endif]--><span style="mso-spacerun:yes"> </span>Clockwise order<o:p></o:p></span></p> <p class="MsoNormal" style="line-height:150%"><span style="mso-ansi-language: EN-US"><span style="mso-tab-count:4"> </span></span><span style="font-family:Symbol;mso-ascii-font-family:"Times New Roman";mso-hansi-font-family: "Times New Roman";mso-ansi-language:EN-US;mso-char-type:symbol;mso-symbol-font-family: Symbol"><span style="mso-char-type:symbol;mso-symbol-font-family:Symbol">\</span></span><span style="mso-ansi-language:EN-US"><span style="mso-tab-count:1"> </span><span style="position:relative;top:6.0pt;mso-text-raise:-6.0pt"><!--[if gte vml 1]><v:shape id="_x0000_i1028" type="#_x0000_t75" style="'width:74.25pt;height:18pt'" ole=""> <v:imagedata src="file:///C:\DOCUME~1\d8\LOCALS~1\Temp\msohtml1\01\clip_image004.wmz" title=""> </v:shape><![endif]--><img width="99" height="24" src="file:///C:/DOCUME~1/d8/LOCALS~1/Temp/msohtml1/01/clip_image005.gif" shapes="_x0000_i1028" /></span><!--[if gte mso 9]><xml> <o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1028" drawaspect="Content" objectid="_1293705750"> </o:OLEObject> </xml><![endif]--><span style="mso-spacerun:yes"> </span>If </span><span lang="EN-GB"><span style="position:relative;top:3.0pt;mso-text-raise:-3.0pt"><!--[if gte vml 1]><v:shape id="_x0000_i1029" type="#_x0000_t75" style="'width:9.75pt;height:14.25pt'" ole=""> <v:imagedata src="file:///C:\DOCUME~1\d8\LOCALS~1\Temp\msohtml1\01\clip_image006.wmz" title=""> </v:shape><![endif]--><img width="13" height="19" src="file:///C:/DOCUME~1/d8/LOCALS~1/Temp/msohtml1/01/clip_image007.gif" shapes="_x0000_i1029" /></span><!--[if gte mso 9]><xml> <o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1029" drawaspect="Content" objectid="_1293705751"> </o:OLEObject> </xml><![endif]--></span><span style="mso-ansi-language:EN-US"><span style="mso-spacerun:yes"> </span>is smaller<o:p></o:p></span></p> <p class="MsoNormal" style="line-height:150%"><span style="mso-ansi-language: EN-US"><span style="mso-tab-count:2"> </span><span style="mso-spacerun:yes"> </span>By using the <st1:place st="on"><st1:city st="on">Newton</st1:city></st1:place>’s Law for the circulation: <o:p></o:p></span></p> <p class="MsoNormal" style="line-height:150%"><span style="mso-ansi-language: EN-US"><o:p> </o:p></span></p> <p class="MsoNormal" style="line-height:150%"><span style="mso-ansi-language: EN-US"><span style="mso-tab-count:2"> </span><span style="mso-spacerun:yes"> </span><span style="position:relative;top:6.0pt; mso-text-raise:-6.0pt"><!--[if gte vml 1]><v:shape id="_x0000_i1043" type="#_x0000_t75" style="'width:78pt;height:18pt'" ole=""> <v:imagedata src="file:///C:\DOCUME~1\d8\LOCALS~1\Temp\msohtml1\01\clip_image008.wmz" title=""> </v:shape><![endif]--><img width="104" height="24" src="file:///C:/DOCUME~1/d8/LOCALS~1/Temp/msohtml1/01/clip_image009.gif" shapes="_x0000_i1043" /></span><!--[if gte mso 9]><xml> <o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1043" drawaspect="Content" objectid="_1293705752"> </o:OLEObject> </xml><![endif]--><o:p></o:p></span></p> <p class="MsoNormal" style="line-height:150%"><span style="mso-ansi-language: EN-US"><span style="mso-tab-count:2"> </span><span style="mso-spacerun:yes"> </span><span style="position:relative;top:6.0pt; mso-text-raise:-6.0pt"><!--[if gte vml 1]><v:shape id="_x0000_i1044" type="#_x0000_t75" style="'width:99.75pt;height:18.75pt'" ole=""> <v:imagedata src="file:///C:\DOCUME~1\d8\LOCALS~1\Temp\msohtml1\01\clip_image010.wmz" title=""> </v:shape><![endif]--><img width="133" height="25" src="file:///C:/DOCUME~1/d8/LOCALS~1/Temp/msohtml1/01/clip_image011.gif" shapes="_x0000_i1044" /></span><!--[if gte mso 9]><xml> <o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1044" drawaspect="Content" objectid="_1293705753"> </o:OLEObject> </xml><![endif]--><o:p></o:p></span></p> <p class="MsoNormal" style="line-height:150%"><span style="mso-ansi-language: EN-US"><span style="mso-tab-count:1"> </span><span style="mso-spacerun:yes"> </span></span><span lang="EN-GB"><span style="position:relative;top:6.0pt;mso-text-raise:-6.0pt"><!--[if gte vml 1]><v:shape id="_x0000_i1045" type="#_x0000_t75" style="'width:90pt;height:18.75pt'" ole=""> <v:imagedata src="file:///C:\DOCUME~1\d8\LOCALS~1\Temp\msohtml1\01\clip_image012.wmz" title=""> </v:shape><![endif]--><img width="120" height="25" src="file:///C:/DOCUME~1/d8/LOCALS~1/Temp/msohtml1/01/clip_image013.gif" shapes="_x0000_i1045" /></span><!--[if gte mso 9]><xml> <o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1045" drawaspect="Content" objectid="_1293705754"> </o:OLEObject> </xml><![endif]--></span><span style="mso-ansi-language:EN-US"><o:p></o:p></span></p> <p class="MsoNormal" style="line-height:150%"><span style="mso-ansi-language: EN-US"><span style="mso-tab-count:2"> </span><span style="mso-spacerun:yes"> </span></span><span lang="EN-GB"><span style="position:relative;top:15.0pt;mso-text-raise:-15.0pt"><!--[if gte vml 1]><v:shape id="_x0000_i1030" type="#_x0000_t75" style="'width:83.25pt;height:33.75pt'" ole=""> <v:imagedata src="file:///C:\DOCUME~1\d8\LOCALS~1\Temp\msohtml1\01\clip_image014.wmz" title=""> </v:shape><![endif]--><img width="111" height="45" src="file:///C:/DOCUME~1/d8/LOCALS~1/Temp/msohtml1/01/clip_image015.gif" shapes="_x0000_i1030" /></span><!--[if gte mso 9]><xml> <o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1030" drawaspect="Content" objectid="_1293705755"> </o:OLEObject> </xml><![endif]--></span></p> <p class="MsoNormal" style="line-height:150%"><span style="mso-ansi-language: EN-US"><o:p> </o:p></span></p> <p class="MsoNormal" style="text-indent:.5in;line-height:150%"><span style="mso-ansi-language:EN-US">You may observe that this equation will be same as the general equation which is “Simple Harmonic Motion”. Therefore, we can obtain the frequency by using this system as followed below:-<o:p></o:p></span></p> <p class="MsoNormal" style="text-indent:.5in;line-height:150%"><span style="mso-ansi-language:EN-US"><o:p> </o:p></span></p> <p class="MsoNormal" style="text-indent:.5in;line-height:150%;tab-stops:1.0in 81.0pt"><span lang="EN-GB"><span style="mso-spacerun:yes"> </span><span style="mso-tab-count: 1"> </span><span style="mso-spacerun:yes"> </span><span style="position:relative;top:15.0pt;mso-text-raise:-15.0pt"><!--[if gte vml 1]><v:shape id="_x0000_i1031" type="#_x0000_t75" style="'width:63.75pt;height:33.75pt'" ole=""> <v:imagedata src="file:///C:\DOCUME~1\d8\LOCALS~1\Temp\msohtml1\01\clip_image016.wmz" title=""> </v:shape><![endif]--><img width="85" height="45" src="file:///C:/DOCUME~1/d8/LOCALS~1/Temp/msohtml1/01/clip_image017.gif" shapes="_x0000_i1031" /></span><!--[if gte mso 9]><xml> <o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1031" drawaspect="Content" objectid="_1293705756"> </o:OLEObject> </xml><![endif]--></span></p> <p class="MsoNormal" style="text-indent:.5in;line-height:150%;tab-stops:1.0in 81.0pt"><span lang="EN-GB"><span style="mso-tab-count:1"> </span><span style="mso-spacerun:yes"> </span><span style="position:relative;top:16.0pt; mso-text-raise:-16.0pt"><!--[if gte vml 1]><v:shape id="_x0000_i1032" type="#_x0000_t75" style="'width:66.75pt;height:38.25pt'" ole=""> <v:imagedata src="file:///C:\DOCUME~1\d8\LOCALS~1\Temp\msohtml1\01\clip_image018.wmz" title=""> </v:shape><![endif]--><img width="89" height="51" src="file:///C:/DOCUME~1/d8/LOCALS~1/Temp/msohtml1/01/clip_image019.gif" shapes="_x0000_i1032" /></span><!--[if gte mso 9]><xml> <o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1032" drawaspect="Content" objectid="_1293705757"> </o:OLEObject> </xml><![endif]--><span style="mso-tab-count:1"> </span><span style="position:relative;top:9.0pt;mso-text-raise:-9.0pt"><!--[if gte vml 1]><v:shape id="_x0000_i1033" type="#_x0000_t75" style="'width:18pt;height:24pt'" ole=""> <v:imagedata src="file:///C:\DOCUME~1\d8\LOCALS~1\Temp\msohtml1\01\clip_image020.wmz" title=""> </v:shape><![endif]--><img width="24" height="32" src="file:///C:/DOCUME~1/d8/LOCALS~1/Temp/msohtml1/01/clip_image021.gif" shapes="_x0000_i1033" /></span><!--[if gte mso 9]><xml> <o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1033" drawaspect="Content" objectid="_1293705758"> </o:OLEObject> </xml><![endif]--></span></p> <p class="MsoNormal" style="line-height:150%;tab-stops:.5in 81.0pt"><span style="mso-ansi-language:EN-US"><span style="mso-tab-count:1"> </span>Mean while, the periodic time (T) is been taken to complete a swinging</span><span style="font-family:Arial;mso-ansi-language:EN-US">, </span><span style="mso-ansi-language:EN-US">therefore:- <span style="position:relative; top:5.0pt;mso-text-raise:-5.0pt"><!--[if gte vml 1]><v:shape id="_x0000_i1034" type="#_x0000_t75" style="'width:9pt;height:17.25pt'" ole=""> <v:imagedata src="file:///C:\DOCUME~1\d8\LOCALS~1\Temp\msohtml1\01\clip_image022.wmz" title=""> </v:shape><![endif]--><img width="12" height="23" src="file:///C:/DOCUME~1/d8/LOCALS~1/Temp/msohtml1/01/clip_image023.gif" shapes="_x0000_i1034" /></span><!--[if gte mso 9]><xml> <o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1034" drawaspect="Content" objectid="_1293705759"> </o:OLEObject> </xml><![endif]--><o:p></o:p></span></p> <p class="MsoNormal" style="text-indent:.5in;line-height:150%;tab-stops:1.0in 81.0pt"><span lang="EN-GB"><span style="mso-tab-count:1"> </span><span style="mso-spacerun:yes"> </span><span style="position:relative;top:12.0pt; mso-text-raise:-12.0pt"><!--[if gte vml 1]><v:shape id="_x0000_i1035" type="#_x0000_t75" style="'width:39.75pt;height:30.75pt'" ole=""> <v:imagedata src="file:///C:\DOCUME~1\d8\LOCALS~1\Temp\msohtml1\01\clip_image024.wmz" title=""> </v:shape><![endif]--><img width="53" height="41" src="file:///C:/DOCUME~1/d8/LOCALS~1/Temp/msohtml1/01/clip_image025.gif" shapes="_x0000_i1035" /></span><!--[if gte mso 9]><xml> <o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1035" drawaspect="Content" objectid="_1293705760"> </o:OLEObject> </xml><![endif]--><span style="mso-spacerun:yes"> </span><span style="mso-tab-count:1"> </span>Seconds</span></p> <p class="MsoNormal" style="text-indent:.5in;line-height:150%;tab-stops:1.0in 81.0pt"><span lang="EN-GB"><span style="mso-spacerun:yes"> </span><span style="position:relative;top:15.0pt;mso-text-raise:-15.0pt"><!--[if gte vml 1]><v:shape id="_x0000_i1036" type="#_x0000_t75" style="'width:81pt;height:36.75pt'" ole=""> <v:imagedata src="file:///C:\DOCUME~1\d8\LOCALS~1\Temp\msohtml1\01\clip_image026.wmz" title=""> </v:shape><![endif]--><img width="108" height="49" src="file:///C:/DOCUME~1/d8/LOCALS~1/Temp/msohtml1/01/clip_image027.gif" shapes="_x0000_i1036" /></span><!--[if gte mso 9]><xml> <o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1036" drawaspect="Content" objectid="_1293705761"> </o:OLEObject> </xml><![endif]--></span></p> <p class="MsoNormal" style="text-indent:.5in;line-height:150%;tab-stops:1.0in 81.0pt"><span lang="EN-GB"><o:p> </o:p></span></p> <p class="MsoNormal" style="text-indent:.5in;line-height:150%;tab-stops:1.0in 81.0pt"><span lang="EN-GB"><o:p> </o:p></span></p> <p class="MsoNormal" style="text-indent:.5in;line-height:150%;tab-stops:1.0in 81.0pt"><span lang="EN-GB"><o:p> </o:p></span></p> <p class="MsoNormal" style="text-indent:.5in;line-height:150%;tab-stops:1.0in 81.0pt"><span lang="EN-GB">For the rigid body, moment of inertia at point O is:</span></p> <p class="MsoNormal" style="line-height:150%;tab-stops:1.0in 81.0pt"><span lang="EN-GB"><o:p> </o:p></span></p> <p class="MsoNormal" style="line-height:150%;tab-stops:1.0in 81.0pt"><span lang="EN-GB"><span style="mso-spacerun:yes"> </span><span style="position: relative;top:6.0pt;mso-text-raise:-6.0pt"><!--[if gte vml 1]><v:shape id="_x0000_i1037" type="#_x0000_t75" style="'width:69.75pt;height:18.75pt'" ole=""> <v:imagedata src="file:///C:\DOCUME~1\d8\LOCALS~1\Temp\msohtml1\01\clip_image028.wmz" title=""> </v:shape><![endif]--><img width="93" height="25" src="file:///C:/DOCUME~1/d8/LOCALS~1/Temp/msohtml1/01/clip_image029.gif" shapes="_x0000_i1037" /></span><!--[if gte mso 9]><xml> <o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1037" drawaspect="Content" objectid="_1293705762"> </o:OLEObject> </xml><![endif]--><span style="mso-spacerun:yes"> </span><span style="mso-tab-count:1"> </span><span style="mso-spacerun:yes"> </span>Where <span style="position:relative;top:6.0pt;mso-text-raise:-6.0pt"><!--[if gte vml 1]><v:shape id="_x0000_i1038" type="#_x0000_t75" style="'width:15pt;height:18pt'" ole=""> <v:imagedata src="file:///C:\DOCUME~1\d8\LOCALS~1\Temp\msohtml1\01\clip_image030.wmz" title=""> </v:shape><![endif]--><img width="20" height="24" src="file:///C:/DOCUME~1/d8/LOCALS~1/Temp/msohtml1/01/clip_image031.gif" shapes="_x0000_i1038" /></span><!--[if gte mso 9]><xml> <o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1038" drawaspect="Content" objectid="_1293705763"> </o:OLEObject> </xml><![endif]--><span style="mso-spacerun:yes"> </span>is the moment of inertia at centre of gravity.</span></p> <p class="MsoNormal" style="line-height:150%;tab-stops:1.0in 81.0pt"><span lang="EN-GB"><span style="position:relative;top:6.0pt;mso-text-raise:-6.0pt"><!--[if gte vml 1]><v:shape id="_x0000_i1039" type="#_x0000_t75" style="'width:87.75pt;height:18.75pt'" ole=""> <v:imagedata src="file:///C:\DOCUME~1\d8\LOCALS~1\Temp\msohtml1\01\clip_image032.wmz" title=""> </v:shape><![endif]--><img width="117" height="25" src="file:///C:/DOCUME~1/d8/LOCALS~1/Temp/msohtml1/01/clip_image033.gif" shapes="_x0000_i1039" /></span><!--[if gte mso 9]><xml> <o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1039" drawaspect="Content" objectid="_1293705764"> </o:OLEObject> </xml><![endif]--><span style="mso-spacerun:yes"> </span><span style="mso-tab-count:1"> </span>Where <span style="position:relative; top:3.0pt;mso-text-raise:-3.0pt"><!--[if gte vml 1]><v:shape id="_x0000_i1040" type="#_x0000_t75" style="'width:9.75pt;height:14.25pt'" ole=""> <v:imagedata src="file:///C:\DOCUME~1\d8\LOCALS~1\Temp\msohtml1\01\clip_image034.wmz" title=""> </v:shape><![endif]--><img width="13" height="19" src="file:///C:/DOCUME~1/d8/LOCALS~1/Temp/msohtml1/01/clip_image035.gif" shapes="_x0000_i1040" /></span><!--[if gte mso 9]><xml> <o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1040" drawaspect="Content" objectid="_1293705765"> </o:OLEObject> </xml><![endif]--><span style="mso-spacerun:yes"> </span>is the radius of gyration at centre of gravity.</span></p> <p class="MsoNormal" style="line-height:150%;tab-stops:1.0in 81.0pt"><span lang="EN-GB"><span style="position:relative;top:15.0pt;mso-text-raise:-15.0pt"><!--[if gte vml 1]><v:shape id="_x0000_i1041" type="#_x0000_t75" style="'width:111.75pt;height:38.25pt'" ole=""> <v:imagedata src="file:///C:\DOCUME~1\d8\LOCALS~1\Temp\msohtml1\01\clip_image036.wmz" title=""> </v:shape><![endif]--><img width="149" height="51" src="file:///C:/DOCUME~1/d8/LOCALS~1/Temp/msohtml1/01/clip_image037.gif" shapes="_x0000_i1041" /></span><!--[if gte mso 9]><xml> <o:oleobject type="Embed" progid="Equation.3" shapeid="_x0000_i1041" drawaspect="Content" objectid="_1293705766"> </o:OLEObject> </xml><![endif]--></span></p> <p class="MsoNormal" style="line-height:150%;tab-stops:1.0in 81.0pt"><span lang="EN-GB"><span style="position:relative;top:15.0pt;mso-text-raise:-15.0pt"><!--[if gte vml 1]><v:shape id="_x0000_i1042" type="#_x0000_t75" style="'width:95.25pt;height:38.25pt'" ole=""> <v:imagedata src="file:///C:\DOCUME~1\d8\LOCALS~1\Temp\msohtml1\01\clip_image038.wmz" title=""> </v:shape><![endif]--><img 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