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  4. A particle executes simple harmonic motion with a frequency f. The frequency with which the potential energy oscillates is:

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Q. A particle executes simple harmonic motion with a frequency $f$. The frequency with which the potential energy oscillates is:

ManipalManipal 2005Oscillations

Solution:

If $ x=A\text{ }sin\text{ }\omega t $
Then, $ PE=\frac{1}{2}m{{A}^{2}}{{\omega }^{2}}{{\sin }^{2}}\omega t $
$ \therefore $ $ PE=\frac{1}{2}m{{A}^{2}}{{\omega }^{2}}\left( \frac{1-\cos 2\omega t}{2} \right) $
$ \therefore $ $ \omega' =2\omega $
Or $ 2\pi f'=2\times 2\pi f $
$ f'=2f $