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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61)  Consider a wire loop with the shape  z=r^2/a + r^4/a^3
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a)  Write the lagrangian for this system.  (be systematic amd careful with
your book-keeping).
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b)  Obtain the Lagrangian eqn of motion...
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c) Solve for all equilibrium positions for this system. Discuss
when they are stable in your opinion.
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d)how does your answer for part c) depend of the spinning frequency, Omega?
Are there different regimes (of Omega).  What defines them?  what is different
about them??
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e)linearize the Lag. eq of mot. around an equilibrium pt and solve for the
frequency of small oscillations.  PLOT your result vs Omega and discuss...
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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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