forced pendulum

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In a review lectures Feynman gave to his freshman students, just before their first big exam, he advised them as follows (copied from Feynman's Tips on Physics, a problem-solving supplement to The Feynman Lectures on Physics):

    "Now, all these things you can feel. You donít have to feel them; you can work them out by making diagrams and calculations, but as problems get more and more difficult, and as you try to understand nature in more and more complicated situations, the more you can guess at, feel, and understand without actually calculating, the much better off you are! So thatís what you should practice doing on the various problems: when you have time somewhere, and youíre not worried about getting the answer for a quiz or something, look the problem over and see if you can understand the way it behaves, roughly, when you change some of the numbers."

Solve the problem given below (originally homework for FLP Vol. I, chapter 23) in the spirit of Feynman's advice, above. It must be solved without using any calculus or differential equations or integral equations or difference equations, etc., without iterative numerical methods, nor any such fancy mathematical tricks! You may use only algebra, geometry, trigonometry, dimensional analysis, and Newtonian mechanics, in your solution, which should be guided by your physical intuition (however note: all intuitions used in solutions must be justified)! Your answer does not have to be exact, but it should at least be a very close approximation. And be sure to show all your work! Here is the problem:

The pivot point of a simple pendulum having a natural period of 1.00 second is moved laterally in a sinusoidal motion with an amplitude 1.00 cm and period 1.10 seconds. With what amplitude should the pendulum bob swing after a steady motion is attained?



Ruggero Altair (html, 7k) (winner of the Feynman Lectures Exercise Challenge)

All Feynman Lectures Exercise Challenge Submissions (pdf, 481k)


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