Homework for Friday, Nov 13.  (due in class on Friday).
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[Also, be sure to work on your POW, due Wdenesday...]
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71)  Consider a wire loop with the shape  z=r^2/a + r^4/a^3  ,
that spins at a frequency Omega...
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a)  Plot the position of the STABLE equilibrium point as a function of
Omega.  (Calculate it first.) 
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b)  If you can, calculate the frequency for small oscillations about the
stable equilibrium point as a function of Omega, AND PLOT IT on a graph
with the position of the stable equilibrium points (both vs Omega).  
If you cannot calculate it, try to do a rough sketch anyway.  What do you learn from
the relationship between these two quantities??
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62)  Consider a double pendulum with equal lengths, l, and masses, m .
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a) Write the Lagrangian, (you have this already)
and obtain from it the Lagrangian equations of motion .
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b)Expand to lowest in order in theta1 and theta2 (for small deviations from
equilibrium).  
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c) Can you solve for the oscillation frequencies of this system (assuming
only small angle  motion)?   How many "normal modes" are there??
What is a normal mode (in general)?
What do you think they look like for this system??
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