In the pendulum problem, = sin pg/l t is an approximate solution when the amplitude is
Chapter 11, Problem 22(choose chapter or problem)
In the pendulum problem, = sin pg/l t is an approximate solution when the amplitude is small enough for the motion to be considered simple harmonic. Show that the corresponding exact solution when is not small is sin 2 = sin 2 snrg l t where k = sin(/2) is the modulus of the elliptic function. Show that this reduces to the simple harmonic motion solution for small amplitude .
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