Homework for Friday, Nov 6.  (due in class on Friday).
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41) Write the Lagrangian for a simple pendulum.
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Obtain the equation of motion from the Lagrangian.
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Expand to lowest in order in theta (for small deviations from
equilibrium).  Solve for x(t).
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42) Write the Lagrangian for a double pendulum.
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Obtain the equation(s) of motion from the Lagrangian.
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Expand to lowest in order in theta1 and theta2 (for small deviations from
equilibrium).  Solve for x(t).
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43) Write the Lagrangian for a bead that moves without friction on
a circular wire loop that spins with frequency Omega.
Get the eqn of motion and solve for the stable and unstable
equilibrium positions...
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43) Write the Lagrangian for a symmetric mass-spring system (two springs, one mass)
mounted on a rotating turntable.
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