Harmonic Motion

<BODY LANG="EN" > <HR><center> <table border=1> <td><A HREF="node69.html"><img height=36 width=36 alt="PREVIOUS" src="/UCESIcons/tools/previous.gif"></A></td> <td><A HREF="node66.html"><img height=36 width=36 alt="UP" src="/UCESIcons/tools/up.gif"></A></td> <td><A HREF="node71.html"><img height=36 width=36 alt="NEXT" src="/UCESIcons/tools/next.gif"></A></td> <td><a href="contents-node70.html"><img height=36 width=36 alt="CONTENTS" src="/UCESIcons/tools/toc.gif"></a></td> </table> </center> <HR> <H2>Harmonic Motion</H2> <P> Many physical models involve motion which is called harmonic. In simple terms, we will say that motion is <B>harmonic</B> if it can be described by either a <IMG WIDTH=17 HEIGHT=12 ALIGN=BOTTOM ALT="sin" SRC="img20.gif"> curve or a <IMG WIDTH=19 HEIGHT=7 ALIGN=BOTTOM ALT="cos" SRC="img21.gif"> curve. Arguably the most obvious example of such motion is that of a spring that is attached at one end and allowed to ``bounce'' up and down. Many children's toys display this sort of motion. Slinkys are well-known for this phenomenon. A yoyo could also be placed in this genre. Even something as complicated as the rise and fall of temperature during the year as the seasons change can be modeled by trigonometric functions. Ultimately, the key lies in the cyclical nature of the model. <P> We note an example here which involves such a cyclical type of problem. <P> <HR><center> <table border=1> <td><A HREF="node69.html"><img height=36 width=36 alt="PREVIOUS" src="/UCESIcons/tools/previous.gif"></A></td> <td><A HREF="node66.html"><img height=36 width=36 alt="UP" src="/UCESIcons/tools/up.gif"></A></td> <td><A HREF="node71.html"><img height=36 width=36 alt="NEXT" src="/UCESIcons/tools/next.gif"></A></td> <td><a href="contents-node70.html"><img height=36 width=36 alt="CONTENTS" src="/UCESIcons/tools/toc.gif"></a></td> </table> </center> <HR><P><ADDRESS> <I><A HREF="http://www.math.psu.edu/sellersj/">James A. Sellers</A> </I> </ADDRESS> </BODY>