Homework for Friday, Oct 23.  (due in class on Friday).
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For this homework, let's start by redoing really well problem
2 from the midterm with the width of the pulse being T/50  (fifty) ,
and problem 3 (from the midterm).
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And in addition, do this problem again...
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(In all this, The * means "times".   The ^ means superscript,  the _ means subscript .
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40) Consider an damped harmonic oscillator driven by the force
F_0*sin^3(wt).
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a) what is the expression for x(t) for this force? 
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b) For beta=.1 and w_0=1, roughly calculate and plot x(t) for w=w_0
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c) For beta=.1 and w_0=1, roughly calculate and plot x(t) for 3*w=w_0
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d) how do the maximum amplitude and the relative phase between the force and
the response compare for these two driving frequencies?  (extra credit)
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41) Write the Lagrangian for a simple pendulum.
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42) Write the Lagrangian for a double pendulum.
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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.
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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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NOTE:  in 41-43 you "just" write the Lagrangian.  You don't have to find or solve
any equations of motion.  (We'll do that later...)