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Q.
A particle executes, simple harmonic motion with a frequency $ f. $ The frequency with which its kinetic energy oscillates is:
Jharkhand CECEJharkhand CECE 2006
Solution:
For a particle executing SHM the displacement equation is given by
$ y=a\sin \omega t=a\sin 2\pi ft. $
kinetic energy $ KE=\frac{1}{2}mv^{2}$
$=\frac{1}{2}m\left( \frac{dy}{dt} \right)^{2} $
where $ \frac{dy}{dt}=2\pi \,fa\,\cos 2\pi \,ft $
$ \therefore KE=\frac{1}{2}m\{(2\pi fa)^{2}\cos ^{2}2\pi ft\} $
$ KE\propto (1+\cos 4\pi ft) $
$ \cos 4\pi ft $ changes periodically with frequency $ 2f. $