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(D) The potential energy $(PE)$ of a particle performing simple harmonic motion $(SHM)$ is given by the expression:$PE = \frac{1}{2} m \omega^2 x^2$wh

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(D) The potential energy $(PE)$ of a particle performing simple harmonic motion $(SHM)$ is given by the expression:$PE = \frac{1}{2} m \omega^2 x^2$where $m$ is the mass,$\omega$ is the angular frequency,and $x$ is the displacement from the equilibrium position $O$.This equation shows that the potential energy varies parabolically with displacement $x$.At the mean position $(x = 0)$,the potential energy is zero.At the extreme positions ($x = x_1$ and $x = x_2$),the potential energy is maximum.Therefore,the graph of potential energy versus displacement is a parabola opening upwards with its vertex at the origin $O$,which corresponds to graph $D$.

$A$ particle of mass $m$ oscillates with simple harmonic motion between points $x_1$ and $x_2$,the equilibrium position being $O$. Its potential energy is plotted. It will be as given below in the graph:

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