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



On 2/19/2011 7:24 AM, David Bowman wrote:
/snip/
Problem:
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.

David Bowman
I sometimes wondered why physicians place so much stock in naming a complaint.
As though the problem is half-resolved at this point.

But today, in musing the labels that go with David's challenge, I notice that 'isochrone' is
one such. Used in a different way to be sure, than when I mentioned three isochronous bobweights on strings. Preferring tautochrone to isochrone for this equal time property, thoughts easily pass to the intriguing brachistochrone curve which provides minimal time between points on a curve.

Having winkled out these labels, my reaction is simply to look them up.
And that deprives the challenge of all challenge. - stripped of all work.
So there is no chance of extra credit, nor even any credit: to do what every student will do because she can: bring to bear the fruits of all knowledge in a moment via Mr. Google or some such.

Brian W