Normal modes

<BODY LANG="EN"> <HR><center> <table border=1> <td><img height=36 width=36 alt="" src="/UCESIcons/tools/previous_fade.gif"></td> <td><A NAME="tex2html2" HREF="Lab4.html"><img height=36 width=36 alt="UP" src="/UCESIcons/tools/up.gif"></A></td> <td><A NAME="tex2html4" HREF="node1.html"><img height=36 width=36 alt="NEXT" src="/UCESIcons/tools/next.gif"></A></td> <td><a href="contents-Lab4.html"><img height=36 width=36 alt="CONTENTS" src="/UCESIcons/tools/toc.gif"></a></td> <td><a href="/hamlet-bin/qhandler?exit" target="results"><img height=36 width=36 alt="RESET" src="/UCESIcons/tools/stop.gif"></a></td> <td><a href="/UCES/hamlet/"><img height=36 width=36 alt="HAMLET" src="/UCESIcons/tools/hamlet.gif"></a></td> <td><a href="copyright.html"><img height=36 width=36 alt="COPYRIGHT" src="/UCESIcons/tools/copyright.gif"></a></td> <td><a href="mailto:uces_info@krellinst.org"><img height=36 width=36 alt="FEEDBACK" src="/UCESIcons/tools/feedback.gif"></a></td> <td><a href="/UCES/hamlet/usage.html"><img height=36 width=36 alt="ABOUT" src="/UCESIcons/tools/about.gif"></a></td> </table> </center> <HR> <P> <H1>Normal modes</H1> <P> (References: Atkins ch. 18.3 and 18.4, Note that this may differ in different editions, use the index! Halliday and Resnick page 410(attached) , Numerical Recipes ch. 11 and 12) <P> In this exercise the vibration of molecules is analyzed using classical mechanics. To motivate and illustrate the concept of normal modes, the vibration of a linear triatomic molecule confined to one dimension is first simulated and then analyzed. Then, the vibrational dynamics in three-dimensions of <IMG WIDTH=30 HEIGHT=22 ALIGN=MIDDLE ALT="tex2html_wrap_inline115" SRC="img1.gif" > and <IMG WIDTH=32 HEIGHT=22 ALIGN=MIDDLE ALT="tex2html_wrap_inline117" SRC="img2.gif" > are simulated. <P> <HR><center> <table border=1> <td><img height=36 width=36 alt="" src="/UCESIcons/tools/previous_fade.gif"></td> <td><A NAME="tex2html2" HREF="Lab4.html"><img height=36 width=36 alt="UP" src="/UCESIcons/tools/up.gif"></A></td> <td><A NAME="tex2html4" HREF="node1.html"><img height=36 width=36 alt="NEXT" src="/UCESIcons/tools/next.gif"></A></td> <td><a href="contents-Lab4.html"><img height=36 width=36 alt="CONTENTS" src="/UCESIcons/tools/toc.gif"></a></td> <td><a href="/hamlet-bin/qhandler?exit" target="results"><img height=36 width=36 alt="RESET" src="/UCESIcons/tools/stop.gif"></a></td> <td><a href="/UCES/hamlet/"><img height=36 width=36 alt="HAMLET" src="/UCESIcons/tools/hamlet.gif"></a></td> <td><a href="copyright.html"><img height=36 width=36 alt="COPYRIGHT" src="/UCESIcons/tools/copyright.gif"></a></td> <td><a href="mailto:uces_info@krellinst.org"><img height=36 width=36 alt="FEEDBACK" src="/UCESIcons/tools/feedback.gif"></a></td> <td><a href="/UCES/hamlet/usage.html"><img height=36 width=36 alt="ABOUT" src="/UCESIcons/tools/about.gif"></a></td> </table> </center> <HR><P><ADDRESS> <I>Hannes Jonsson<BR> Modified by Thomas L. Marchioro II<BR> and the <A NAME="tex2html1" HREF="/UCES/">Undergraduate Computational Engineering and Science project</A> </I> </ADDRESS> </BODY>