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November 16th, 2016, 07:09 AM   #1
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The equation of motion of an undamped pendulum (i.e., there is no friction) is

mLy''-mgsin(y)

The pendulum is made by attaching a weight of mass m to a very light and
rigid rod of length L mounted on a pivot so that the system can swing in a
vertical plane. Here y denotes the angle that the pendulum makes with the
vertical (equilibrium) position and g is the acceleration of gravity. Note that
−π/2 < y < π/2. The restoring force, due to gravity, is fre(y) = −mg sin y

A) find the potential energy p(y)
B) Find the mechanical energy E(t)

So far all I have done is solved for y'' and got y''=(-g/L)sin(y), I have no idea where to begin to begin finding the potential or mechanical energy of the pendulum.
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November 16th, 2016, 08:14 AM   #2
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The general problem cannot be solved analytically for x(t) or v(t), which is why the question is asking for energy rather than x(t) or v(t). To answer the questions, find out what the formulae for potential energy and kinetic energy are and try to substitute those into the ODE you have before solving.
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