<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 {color: #0033CC; font-weight: bold; } --> </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" 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<param name="Buttons" value="about=no config=no init=yes clear=yes"> <param name="E_00" value="fixed='yes' bg_display='topleft' background='d7d7d7' net='no' net10='no' axes='gray' text='white' x-axis='t' y-axis='a' numbers='yes'"> <param name="C_00" value="type='num&eacute;rico' id='Ox' region='external' value='-150' decimals='0' fixed='yes' name='O.x' incr='32' visible='no'"> <param name="C_01" value="type='num&eacute;rico' id='Oy' gui='spinner' region='external' value='-20' fixed='yes' incr='32' action=' '"> <param name="C_02" value="type='num&eacute;rico' id='A' gui='spinner' region='south' value='10' decimals='0' fixed='yes' name='A' incr='1' inf='0' sup='15' action=' '"> <param name="C_03" value="type='num&eacute;rico' id='T' gui='spinner' region='south' value='7' decimals='1' fixed='yes' name='T' incr='0.2' inf='1' sup='7' action=' '"> <param name="C_04" value="type='num&eacute;rico' id='Escena' gui='button' region='north' fixed='yes' name='Visual' tooltip='Descripci&oacute;n (left-click for more information)' Explanation='Descripci&oacute;n (left-click for more information)' action='message' parameter='This visual represents the acceleration vector.\nThe graph represents the value of acceleration (vertical axis) versus time (horizontal axis).'"> <param name="C_05" value="type='num&eacute;rico' id='A1' gui='button' region='north' fixed='yes' name='A1' tooltip='Activity 1 (left-click for more information)' Explanation='Activity 1 (left-click for more information)' action='message' parameter='The acceleration vector is always tangent to the trajectory in this movement and its orientation depends on the elongation. When is the sign of the acceleration positive? When is it negative?'"> <param name="C_06" value="type='num&eacute;rico' id='A2' gui='button' region='north' fixed='yes' name='A2' tooltip='Activity 1 (left-click for more information)' Explanation='Activity 1 (left-click for more information)' action='message' parameter='By looking at the graph and the vector, determine the positions in which the acceleration is maximum and minimum.'"> <param name="C_07" value="type='num&eacute;rico' id='escala' region='north' value='10' decimals='0' fixed='yes' name='zoom' incr='1' inf='1' sup='1000000' visible='no'"> <param name="A_00" value="id='w' expresion='(2*pi)/T'"> <param name="A_01" value="id='pi' expresion='3.14159' evaluate='only-once' constant='yes'"> <param name="A_02" value="id='y' expresion='A*(sen(w*t))'"> <param name="A_03" value="id='f' expresion='1/T'"> <param name="A_04" value="id='ac' expresion='-A*w*w*(sen(w*t))'"> <param name="A_05" value="id='a(x)' expresion='((x*17)-100-Ox)/escala'"> <param name="A_06" value="id='b(x)' expresion='((x*17)+Oy)/escala'"> <param name="A_07" value="id='v' expresion='A*w*(cos(w*t))'"> <param name="G_00" value="type='equation' draw-if='(x>0)&(x<20)' colour='a572a8' expresion='y=-A*w*w*sen(w*x)' visible='no'"> <param name="G_01" value="type='segment' colour='8d7d7d' expresion='(-5,-A)(-5,A)' fixed='yes'"> <param name="G_02" value="type='polygon' background='yes' colour='a24040' expresion='(a(12),b(-5))(a(18),b(-5))(a(18),b(-6.7))(a(12),b(-6.7))(a(12),b(-5))' fill='white' width='4'"> <param name="G_03" value="type='segment' colour='750075' expresion='(0+t,0)(0+t,ac)' text='a' font='Helvetica,BOLD,14' fixed='yes'"> <param name="G_04" value="type='segment' colour='a24040' expresion='(-7,0)(-7,A)' fixed='yes'"> <param name="G_05" value="type='text' colour='a24040' expresion='[355,225]' text='t=[t]s' font='Courier,BOLD,14' fixed='yes'"> <param name="G_06" value="type='text' colour='750075' expresion='[80,220]' text='{\rtf1\uc0{\fonttbl\f0\fcharset0 Arial;}\f0\fs32\b a=- A\u183 \u969 {\*\mjaformula{\supix 2}}\u183 sin(\u969 \u183 t)= {\*\mjaformula{\expr ac}} m/s{\*\mjaformula{\supix 2}}\par}' font='SantSerif,BOLD,16' fixed='yes'"> <param name="G_07" value="type='text' colour='a24040' expresion='[10,60]' text='A' fixed='yes'"> <param name="G_08" value="type='text' colour='black' expresion='[350,20]' text='Æ = [f] Hz' font='Courier,PLAIN,14' fixed='yes'"> <param name="G_09" value="type='text' colour='black' expresion='[350,40]' text='É = [w] rad/s' font='Monospaced,PLAIN,14' fixed='yes'"> <param name="G_10" value="type='arrow' draw-if='(t>0)&(t<20)' colour='750075' expresion='(-5,y)(-5,y+ac)' text='a' font='Helvetica,BOLD,14' fixed='yes' width='2' width='2' spear='4' arrow='750075'"> <param name="G_11" value="type='point' colour='red' expresion='(-5,y)' fixed='yes' size='6'"> <param name="G_12" value="type='point' colour='750075' expresion='(0+t,ac)' trace='a52aa8' fixed='yes' size='4'"> <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> &nbsp;</P> <div align="justify"> <FONT size=3><FONT size=3></FONT></FONT></div></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> 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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="eltoSubMenuHead20" align="left" bgcolor="#ffffff" width="123"><a class="clsMenu" href="javascript:enlace('31_mas.html', 2, 0)">Elastic force</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="eltoSubMenuHead21" align="left" bgcolor="#f0f0f0" width="123"><a class="clsMenu" href="javascript:enlace('32_mas.html', 2, 1)">Frequency</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="eltoSubMenuHead22" align="left" bgcolor="#ffffff" width="123"><a class="clsMenu" href="javascript:enlace('33_mas.html', 2, 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="eltoMenu3" nombre="eltoMenu3"> <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="eltoMenuHead3" align="left" bgcolor="#e48ca2" height="25" width="112"><a class="clsMenu" href="javascript:gestionMenu(3)">The energy 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="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 class="clsMenu" href="51_mas.html">Evaluation</a></td> <td 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