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Re: [Phys-l] Another practical problem (challenge problem)



On 02/19/2011 06:24 AM, David Bowman wrote:
Suppose you are allowed to change the shape of the bowl from a
circle/sphere to some other concave shape that causes the resulting
period of the sliding mass to actually execute true simple harmonic
motion for any amplitude (within reason) when the motion is still in
a vertical plane. Question: What is the shape that the bowl must
have for this to work out? Extra credit: After you have found this
curve/shape, is there some way, in hindsight, whereby you could have
figured out the shape without doing all that work? Stipulation: The
amplitude of the motion is to be measured by the path length traveled
by the mass/bob for whatever path shape is to be used.

I seem to recall some Dutch guy was interested in this problem.
He found a way to solve it without using calculus, and without
using Newton's laws of motion ... which stands to reason, because
his solution predated the _Principia_ by several years.