midterm2 - % BB Mar 10 2010 \documentclass[12pt]cfw_article...

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% BB Mar 10 2010 \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 MAKE UP MIDTERM ADVANCED DYNAMICS --- PHY--4241/5227}\\ % \vspace {1mm}{March 17, 2010} \\ \end{center} \setcounter{equation}{0} \bigskip %%%%%%%%%%%%%%%%%%%%%%%%%% \centerline{\bf PROBLEM 1 (20 points)} \medskip \noindent Let the interaction of two point particles be described by the Lagrangian $$ L = \frac{m_1}{2}\dot{\vec{r}}_1^{\,2} + \frac{m_2}{2}\dot{\vec{r}}_2^{\,2} - \frac{k}{2}\,\left(\vec{r}_1-\vec{r}_2\right)^2\,. $$ \begin{enumerate} \item Is the energy of this system conserved (with reason)? \item Write down the definition of the center of mass $\vec{R}(t)$
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midterm2 - % BB Mar 10 2010 \documentclass[12pt]cfw_article...

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