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(C) The displacement equation for a simple harmonic motion $(SHM)$ with frequency $n$ is given by:$x = A \sin(\omega t) = A \sin(2 \pi n t)$The potent

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$2n$

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(C) The displacement equation for a simple harmonic motion $(SHM)$ with frequency $n$ is given by:$x = A \sin(\omega t) = A \sin(2 \pi n t)$The potential energy $(U)$ of the body is given by:$U = \frac{1}{2} k x^2 = \frac{1}{2} k A^2 \sin^2(2 \pi n t)$Using the trigonometric identity $\sin^2 	heta = \frac{1 - \cos(2 	heta)}{2}$,we get:$U = \frac{1}{2} k A^2 \left[ \frac{1 - \cos(2 \cdot 2 \pi n t)}{2} ight] = \frac{1}{4} k A^2 [1 - \cos(4 \pi n t)]$The frequency of the potential energy is the coefficient of $2 \pi t$ in the cosine term,which is $2n$.

$A$ body is executing simple harmonic motion with frequency $n$,the frequency of its potential energy is:

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