Question 88 of 194

The variation of displacement with time of a particle executing free simple harmonic motion is shown in the figure.

The potential energy $U(x)$ versus time $\left(t\right)$ plot of the particle is correctly shown in figure:

ABCD

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Answer: (D)

Considering$\rightarrow$ Spring $-$ mass system
$x={x}_{0}\sin \omega t$
$P.E.=\dfrac{1}{2}k{x}^{2}=\dfrac{1}{2}kx{o}^{2}{\sin }^{2}\omega t=c{\sin }^{2}\omega t$
$\Rightarrow PE=\left(\dfrac{1-\cos 2\omega t}{2}\right)$