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(D) In simple harmonic motion,the displacement of the particle is given by $x(t) = x_0 \sin(\omega t + \phi)$.The velocity of the particle is $v = \fr

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(D) In simple harmonic motion,the displacement of the particle is given by $x(t) = x_0 \sin(\omega t + \phi)$.The velocity of the particle is $v = \frac{dx}{dt} = x_0 \omega \cos(\omega t + \phi)$.The probability $P(x) dx$ of finding the particle in the interval $(x, x + dx)$ is proportional to the time $dt$ it spends in that interval,which is $P(x) \propto \frac{dt}{dx} = \frac{1}{|v|}$.Since $v = \omega \sqrt{x_0^2 - x^2}$,we have $P(x) \propto \frac{1}{\sqrt{x_0^2 - x^2}}$.This function has a minimum at the mean position $(x = 0)$ and approaches infinity at the extreme positions $(x = \pm x_0)$.Graph $D$ shows the number of events (which is proportional to the probability density) being lowest at the center and increasing towards the extreme positions,which matches the behavior of the function $P(x) \propto \frac{1}{\sqrt{x_0^2 - x^2}}$.

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