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I have a rather ambitious student who, for a Senior project, is attempting
to analyze the motion of a driven damped pendulum. We have gone through the
more simple case of a mass on a spring found in most texts.
He has developed a 2nd order differential (using Newton's 2nd law) to
describe
the motion and is now attempting to solve it. Does anyone have any ideas for
arriving at a mathematical expression for the pendulum's angular displacement
as a function of time? (I have plenty of ideas, but won't bore you with the
details ... yet.)