<HTML> <HEAD> <META http-equiv=Content-Type content='text/html; charset=ISO-8859-1'> <TITLE>Simple harmonic movement</TITLE> <LINK REL="stylesheet" TYPE="text/css" HREF="../css/newton.css"> <script type="text/javascript" language="JavaScript" src="../js/objNavegador.js"></script> <script type="text/javascript" language="JavaScript" src="../js/objLayer.js"></script> <script type="text/javascript" language="JavaScript" src="../js/newton.js"></script> <style type="text/css"> <!-- .Estilo1 {font-size: 14px} .Estilo2 { color: #0033CC; font-weight: bold; } .Estilo3 {color: #000000} .Estilo4 {font-size: 14px; color: #000000; } --> </style> </HEAD> <body onload="posicionaMenu(5)" bgcolor="#ffffff"> <div class="clsCurso" id="CapaCurso" contenteditable="false" gblcoloron="FFACC2" gblcolor="E48CA2">2<sup>nd</sup> year of post-compulsory secondary education</div> <div id="CapaFondo"><img src="images/fondo.jpg" height="429" width="770"></div> <div id="CapaImg"><img id="imgUnidad" src="images/mas.gif" name="imgUnidad"></div> <div id="eltoMenuHead" nombre="eltoMenuHead"> <table border="0" cellpadding="0" cellspacing="0" width="138"> <tbody> <tr> <td><img src="images/menu/menu_01.jpg" height="4" width="10"></td> <td><img src="images/menu/menu_02.jpg" height="4" width="112"></td> <td><img src="images/menu/menu_03.jpg" height="4" width="16"></td> </tr> <tr> <td background="images/menu/menu_04.jpg" height="29" width="10"></td> <td class="clsMenuHead" id="tbMenuVTitulo" align="center" bgcolor="#f7f7f7" height="29" width="112"><a href="mas.html"><font class="clsMenuHead">Simple Harmonic Movement</font></a></td> <td background="images/menu/menu_06.jpg" height="29" width="16"></td> </tr> <tr> <td><img src="images/menu/menu_07.jpg" height="2" width="10"></td> <td><img src="images/menu/menu_08.jpg" height="2" width="112"></td> <td><img src="images/menu/menu_09.jpg" height="2" width="16"></td> </tr> <tr> <td><img src="images/menu/menu_10.jpg" height="2" width="10"></td> 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codebase="../../" archive="Descartes3.jar" MAYSCRIPT width=450 height=340> <param name="name" value="Desfase"> <param name="Version" value="3.506"> <param name="Language" value="english"> <param name="Buttons" value="about=no config=no init=yes clear=no"> <param name="E_00" value="fixed='yes' bg_display='topleft' background='d7d7d7' net='no' net10='no' axes='gray' text='white' y-axis='Y' numbers='yes'"> <param name="C_00" value="type='num&eacute;rico' id='escala' region='external' value='17' decimals='0' fixed='yes' name='zoom' incr='1' inf='1' sup='1000000' visible='no'"> <param name="C_01" value="type='num&eacute;rico' id='Ox' region='external' value='-80' decimals='0' fixed='yes' name='O.x' incr='32' visible='no'"> <param name="C_02" value="type='num&eacute;rico' id='Oy' region='external' value='-10' decimals='0' fixed='yes' name='O.y' incr='32' visible='no'"> <param name="C_03" value="type='num&eacute;rico' id='A' region='external' value='6.5' decimals='0' fixed='yes' name='A' 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Therefore, either of them can be chosen and the example no longer illustrates the point.'"> <param name="C_11" value="type='num&eacute;rico' id='sent' gui='choice' value='+1' decimals='0' fixed='yes' name='Direction' visible='no' options='Up[1],Down[-1]'"> <param name="C_12" value="type='num&eacute;rico' id='Caux' value='1' decimals='0' fixed='yes' name='auxiliary body' incr='1' inf='1' sup='2'"> <param name="A_00" value="id='pi' expresion='3.14159' evaluate='only-once' constant='yes'"> <param name="A_01" value="id='w' expresion='(2*pi)/T'"> <param name="A_02" value="id='f' expresion='1/T'"> <param name="A_03" value="id='a(x)' expresion='((x*17)-100-Ox)/escala'"> <param name="A_04" value="id='b(x)' expresion='((x*17)+Oy)/escala'"> <param name="A_05" value="id='grad(x)' expresion='(x*180)/pi'"> <param name="A_06" value="id='g1' expresion='asen(y0.y/A)'"> <param name="A_07" value="id='g2' expresion='pi-g1'"> <param name="A_08" value="id='xa' expresion='A*(cos(w*t+g1))'"> <param 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value="type='segment' draw-if='sent=-1' expresion='(0,0)(0,yb)' text='y' fixed='yes' width='3'"> <param name="G_06" value="type='segment' draw-if='(sent=1)|((t<5)&(sent=-1))' colour='white' expresion='(0,ya)(xa,ya)' fixed='yes' width='3'"> <param name="G_07" value="type='segment' draw-if='(sent=-1)|((t<5)&(sent=1))' colour='white' expresion='(0,yb)(xb,yb)' fixed='yes' width='3'"> <param name="G_08" value="type='segment' draw-if='(sent=1)|((t<5)&(sent=-1))' colour='darkGray' expresion='(0,0)(xa,ya)' fixed='yes'"> <param name="G_09" value="type='segment' draw-if='(sent=-1)|((t<5)&(sent=1))' colour='be00c3' expresion='(0,0)(xb,yb)' fixed='yes'"> <param name="G_10" value="type='text' colour='a24040' expresion='[327,262]' text='t=[t]s' font='Courier,BOLD,14' fixed='yes'"> <param name="G_11" value="type='text' expresion='[70,270]' text='y= A&middot;sin (É&middot;t+Æ)= [ya] m' font='SantSerif,BOLD,16' fixed='yes'"> <param name="G_12" value="type='text' colour='red' expresion='[290,210]' text='Real body' fixed='yes'"> <param name="G_13" value="type='text' colour='be00c3' expresion='[290,230]' text='auxiliary bodies' fixed='yes'"> <param name="G_14" value="type='arrow' draw-if='(sent=1) & (t>0)& (t<20)' colour='006a00' expresion='(0,ya)(0,ya+(v1/2))' fixed='yes' width='2' width='2' spear='4' arrow='006a00'"> <param name="G_15" value="type='arrow' draw-if='(sent=-1) & (t>0)& (t<20)' colour='006a00' expresion='(0,yb)(0,yb+(v2/2))' fixed='yes' width='2' width='2' spear='4' arrow='006a00'"> <param name="G_16" value="type='point' draw-if='sent=1' colour='red' expresion='(0,ya)' fixed='yes' size='6'"> <param name="G_17" value="type='point' draw-if='sent=-1' colour='red' expresion='(0,yb)' fixed='yes' size='6'"> <param name="G_18" value="type='point' draw-if='(sent=1)|((t<5)&(sent=-1))' colour='darkGray' expresion='(xa,ya)' text=' 1' fixed='yes' size='5'"> <param name="G_19" value="type='point' draw-if='(sent=-1)|((t<5)&(sent=1))' colour='be00c3' expresion='(xb,yb)' text=' 2' fixed='yes' size='5'"> <param name="G_20" value="type='text' draw-if='(sent=1)|((t<5)&(sent=-1))' colour='darkGray' expresion='[310,60]' text='{\rtf1\uc0{\fonttbl\f0\fcharset0 Courier New;}\f0\fs24\b\u966 {\*\mjaformula{\subix 1}}={\*\mjaformula{\expr g1}} rad\fs32\par}' font='Monospaced,BOLD,12' fixed='yes'"> <param name="G_21" value="type='text' draw-if='(sent=-1)|((t<5)&(sent=1))' colour='be00c3' expresion='[310,80]' text='{\rtf1\uc0{\fonttbl\f0\fcharset0 Courier New;}\f0\fs28\b\u966 {\*\mjaformula{\subix 2}}={\*\mjaformula{\expr g2}} rad\par}' font='Monospaced,BOLD,14' fixed='yes'"> <param name="G_22" value="type='text' draw-if='((sent=1)&(Caux=1)&(t>3))|((sent=-1)&(Caux=2)&(t>3))' colour='00a000' expresion='[290,20]' text='Well done !!' font='Helvetica,BOLD,16' fixed='yes'"> <param name="G_23" value="type='text' draw-if='((sent=1)&(Caux=1)&(t>3))|((sent=-1)&(Caux=2)&(t>3))' colour='00a000' expresion='[250,40]' text='You chose the correct body' fixed='yes'"> <param name="G_24" value="type='text' draw-if='((sent=1)&(Caux=2)&(t>3))|((sent=-1)&(Caux=1)&(t>3))' colour='red' expresion='[280,20]' text='Incorrect' font='Helvetica,BOLD,16' fixed='yes'"> <param name="G_25" value="type='text' draw-if='((sent=1)&(Caux=2)&(t>3))|((sent=-1)&(Caux=1)&(t>3))' colour='red' expresion='[275,40]' text='Try again' fixed='yes'"> <param name="G_26" value="type='point' colour='red' expresion='(8,-4.8)' fixed='yes' size='4'"> <param name="G_27" value="type='point' colour='darkGray' expresion='(8,-6)' fixed='yes' size='4'"> <param name="G_28" value="type='point' colour='be00c3' expresion='(7.3,-6)' fixed='yes' size='4'"> <param name="G_29" value="type='text' draw-if='(t=0)&((y0.y=A)|(y0.y=-A))' colour='red' expresion='[210,20]' text='Choose another position' font='Helvetica,BOLD,16' fixed='yes'"> <param name="Animation" value="delay='100' controls='no' auto='no' init='n=0; t=0' do='n=n+1;t=n/10' while='n<=199'"> </applet> </P> <P align="justify" class="Estilo1 Estilo3">&nbsp; </P> <FONT size=3>&nbsp;</FONT></TD> </TR> </TABLE> </TD> </TR></TABLE> <TABLE id=oTblSep0 height=1 cellSpacing=0 cellPadding=0 border=0> <TR height=1> <TD height=1></TD></TR></TABLE></DIV> <div class="clsCapasMenu" id="eltoMenu0" nombre="eltoMenu0"> <table border="0" cellpadding="0" cellspacing="0" width="138"> <tbody> <tr> <td><img src="images/menu/menu_19.jpg" height="2" width="10"></td> <td><img src="images/menu/menu_20.jpg" height="2" width="112"></td> <td><img src="images/menu/menu_21.jpg" height="2" width="16"></td> </tr> <tr> <td background="images/menu/menu_22.jpg" height="25" width="10"><img src="images/spacer.gif" height="1" width="1"></td> <td class="clsMenu" id="eltoMenuHead0" align="left" bgcolor="#e48ca2" height="25" width="112"><a class="clsMenu" href="javascript:gestionMenu(0)">Introduction</a></td> <td background="images/menu/menu_24.jpg" height="25" width="16"><img src="images/spacer.gif" height="1" width="1"></td> </tr> <tr> <td><img src="images/menu/menu_25.jpg" height="4" width="10"></td> <td><img src="images/menu/menu_26.jpg" height="4" width="112"></td> <td><img src="images/menu/menu_27.jpg" height="4" width="16"></td> </tr> </tbody> </table> <table align="center" border="0" bordercolor="#ffffff" cellpadding="2" cellspacing="0" width="138"> <tbody> <tr> <td width="5"><img src="images/spacer.gif" height="1" width="5"></td> <td class="clsSubMenu" id="eltoSubMenuHead00" align="left" bgcolor="#ffffff" width="123"><a class="clsMenu" href="javascript:enlace('11_mas.html', 0, 0)">Definitions</a></td> <td width="5"><img src="images/spacer.gif" height="1" width="10"></td> </tr> <tr> <td width="5"><img src="images/spacer.gif" height="1" width="5"></td> <td class="clsSubMenu" id="eltoSubMenuHead01" align="left" bgcolor="#f0f0f0" width="123"><a class="clsMenu" href="javascript:enlace('12_mas.html', 0, 1)">Representing the S.H.M.</a></td> <td width="5"><img src="images/spacer.gif" height="1" width="10"></td> </tr> </tbody> </table> </div> <div class="clsCapasMenu" id="eltoMenu1" nombre="eltoMenu1"> <table border="0" cellpadding="0" cellspacing="0" width="138"> <tbody> <tr> <td><img src="images/menu/menu_19.jpg" height="2" width="10"></td> <td><img src="images/menu/menu_20.jpg" height="2" width="112"></td> <td><img src="images/menu/menu_21.jpg" height="2" width="16"></td> </tr> <tr> <td background="images/menu/menu_22.jpg" height="25" width="10"><img src="images/spacer.gif" height="1" width="1"></td> <td class="clsMenu" id="eltoMenuHead1" align="left" bgcolor="#e48ca2" height="25" width="112"><a class="clsMenu" href="javascript:gestionMenu(1)">The kinematics of an S.H.M.</a></td> <td background="images/menu/menu_24.jpg" height="25" width="16"><img src="images/spacer.gif" height="1" width="1"></td> </tr> <tr> <td><img src="images/menu/menu_25.jpg" height="4" width="10"></td> <td><img src="images/menu/menu_26.jpg" height="4" width="112"></td> <td><img src="images/menu/menu_27.jpg" height="4" width="16"></td> </tr> </tbody> </table> <table align="center" border="0" bordercolor="#ffffff" cellpadding="2" cellspacing="0" width="138"> <tbody> <tr> <td width="5"><img src="images/spacer.gif" height="1" width="5"></td> <td class="clsSubMenu" id="eltoSubMenuHead10" align="left" bgcolor="#ffffff" width="123"><a class="clsMenu" href="javascript:enlace('21_mas.html', 1, 0)">Position</a></td> <td width="5"><img src="images/spacer.gif" height="1" width="10"></td> </tr> <tr> <td width="5"><img src="images/spacer.gif" height="1" width="5"></td> <td class="clsSubMenu" id="eltoSubMenuHead11" align="left" bgcolor="#f0f0f0" width="123"><a class="clsMenu" href="javascript:enlace('22_mas.html', 1, 1)">Velocity</a></td> <td width="5"><img src="images/spacer.gif" height="1" width="10"></td> </tr> <tr> <td width="5"><img src="images/spacer.gif" height="1" width="5"></td> <td class="clsSubMenu" id="eltoSubMenuHead12" align="left" bgcolor="#ffffff" width="123"><a class="clsMenu" href="javascript:enlace('23_mas.html', 1, 2)">Acceleration</a></td> <td width="5"><img src="images/spacer.gif" height="1" width="10"></td> </tr> <tr> <td width="5"><img src="images/spacer.gif" height="1" width="5"></td> <td class="clsSubMenu" id="eltoSubMenuHead13" align="left" bgcolor="#f0f0f0" width="123"><a class="clsMenu" href="javascript:enlace('24_mas.html', 1, 3)">S.H.M. and Uniform Circular Movement</a></td> <td width="5"><img src="images/spacer.gif" height="1" width="10"></td> </tr> <tr> <td width="5"><img src="images/spacer.gif" height="1" width="5"></td> <td class="clsSubMenu" id="eltoSubMenuHead14" align="left" bgcolor="#ffffff" width="123"><a class="clsMenu" href="javascript:enlace('25_mas.html', 1, 4)">Phase</a></td> <td width="5"><img src="images/spacer.gif" height="1" width="10"></td> </tr> <tr> <td width="5"><img src="images/spacer.gif" height="1" width="5"></td> <td class="clsSubMenu" id="eltoSubMenuHead15" align="left" bgcolor="#f0f0f0" width="123"><a class="clsMenu" href="javascript:enlace('26_mas.html', 1, 5)">Conclusions</a></td> <td width="5"><img src="images/spacer.gif" height="1" width="10"></td> </tr> </tbody> </table> </div> <div class="clsCapasMenu" id="eltoMenu2" nombre="eltoMenu2"> <table border="0" cellpadding="0" cellspacing="0" width="138"> <tbody> <tr> <td><img src="images/menu/menu_19.jpg" height="2" width="10"></td> <td><img src="images/menu/menu_20.jpg" height="2" width="112"></td> <td><img src="images/menu/menu_21.jpg" height="2" width="16"></td> </tr> <tr> <td background="images/menu/menu_22.jpg" height="25" width="10"><img src="images/spacer.gif" height="1" width="1"></td> <td class="clsMenu" id="eltoMenuHead2" align="left" bgcolor="#e48ca2" height="25" width="112"><a class="clsMenu" href="javascript:gestionMenu(2)">The dynamics of an S.H.M.</a></td> <td background="images/menu/menu_24.jpg" height="25" width="16"><img src="images/spacer.gif" height="1" width="1"></td> </tr> <tr> <td><img src="images/menu/menu_25.jpg" height="4" width="10"></td> <td><img 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src="images/spacer.gif" height="1" width="1"></td> </tr> <tr> <td><img src="images/menu/menu_25.jpg" height="4" width="10"></td> <td><img src="images/menu/menu_26.jpg" height="4" width="112"></td> <td><img src="images/menu/menu_27.jpg" height="4" width="16"></td> </tr> </tbody> </table> <table align="center" border="0" bordercolor="#ffffff" cellpadding="2" cellspacing="0" width="138"> <tbody> <tr> <td width="5"><img src="images/spacer.gif" height="1" width="5"></td> <td class="clsSubMenu" id="eltoSubMenuHead30" align="left" bgcolor="#ffffff" width="123"><a class="clsMenu" href="javascript:enlace('41_mas.html', 3, 0)">Conservation of energy</a></td> <td width="5"><img src="images/spacer.gif" height="1" width="10"></td> </tr> <tr> <td width="5"><img src="images/spacer.gif" height="1" width="5"></td> <td class="clsSubMenu" id="eltoSubMenuHead31" align="left" bgcolor="#f0f0f0" width="123"><a class="clsMenu" href="javascript:enlace('42_mas.html', 3, 1)">Graphic representation</a></td> <td width="5"><img src="images/spacer.gif" height="1" width="10"></td> </tr> <tr> <td width="5"><img src="images/spacer.gif" height="1" width="5"></td> <td class="clsSubMenu" id="eltoSubMenuHead32" align="left" bgcolor="#ffffff" width="123"><a class="clsMenu" href="javascript:enlace('43_mas.html', 3, 2)">Conclusions</a></td> <td width="5"><img src="images/spacer.gif" height="1" width="10"></td> </tr> </tbody> </table> </div> <div class="clsCapasMenu" id="eltoMenu4" nombre="eltoMenu4"> <table border="0" cellpadding="0" cellspacing="0" width="138"> <tbody> <tr> <td><img src="images/menu/menu_19.jpg" height="2" width="10"></td> <td><img src="images/menu/menu_20.jpg" height="2" width="112"></td> <td><img src="images/menu/menu_21.jpg" height="2" width="16"></td> </tr> <tr> <td background="images/menu/menu_22.jpg" height="25" width="10"><img src="images/spacer.gif" height="1" width="1"></td> <td class="clsMenu" id="eltoMenuHead4" align="left" bgcolor="#e48ca2" height="25" width="112"><a 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