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 problemsolving supplement to The Feynman Lectures on Physics):
"Now, all these things you can feel. You don’t 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 that’s what you should practice
doing on the various problems: when you have time somewhere, and you’re 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?
Answer :
Solutions
Ruggero
Altair (html,
7k) (winner of the Feynman Lectures
Exercise Challenge)
All Feynman Lectures Exercise Challenge Submissions (pdf, 481k)
