# midterm - % BB 2-25-04 \documentclass[12pt]cfw_article...

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% BB 2-25-04 \documentclass[12pt]{article} \textheight 9.5in \textwidth 6.0in \topmargin -0.7in \headsep 0.4in \oddsidemargin 0.25in \evensidemargin 0.25in \def\pmbf#1{{\mbox{\boldmath${#1}$}}} \def\undertext#1{$\underline{\smash{\hbox{#1}}}$} \pagestyle{empty} \begin{document} %----------------------------------------------------% %%%%%%%%%%%%%%%%% ADVANCED DYNAMICS %%%%%%%%%%%%%%%% %----------------------------------------------------% \begin{center} {\bf MIDTERM ADVANCED DYNAMICS --- PHY--4241/5227}\\ \vspace {1mm}{March 6, 2009} \\ \end{center} \setcounter{equation}{0} \bigskip %%%%%%%%%%%%%%%%%%%%%%%%%% \centerline{\bf PROBLEM 1 (20 points)} \medskip \noindent The Lagrangian of the 1D harmonic oscillator is $$L={1\over 2}\,m\,\dot{x}^2-{1\over 2}\,k\,x^2\ .$$ \begin{enumerate} \item Find the momentum $p$. \item Write down the Hamiltonian $H(p,x)$. \item Write down Hamilton's equations. \item Show that Hamilton's equations give Newton's force law.

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## midterm - % BB 2-25-04 \documentclass[12pt]cfw_article...

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