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1bigman
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Homework Statement
We have a light rigid pendulum with length ##l##. A mass ##M## is placed at the end and a mass ##m## is placed a distance ##x## from the pivot. What is the period of the pendulum?
Homework Equations
The Attempt at a Solution
Reduce the problem to a single mass situation using the center of mass. From the pivot, I get the center of mass ##r = \frac{mx+Ml}{m+M}##
Using the small angle approximation we end up with ##\frac{d^2\theta}{dt^2} + \frac{g(M+m)}{mx + Ml} \theta = 0## and hence ## T = 2\pi \sqrt{\frac{mx + Ml}{g(M+m)}}##
I suspect this is incorrect as the second part of the questions asks for the value of ##x## which has the greatest impact on ##T## which cannot be obtained as ##\frac{dT}{dx} = 0 ## has no solutions in ##0<x<l##. Help is much appreciated.