Consider a one-dimensional potential $V(x)$ as shown in the figure below. A classical particle of mass $m$ moves under its influence and has total energy $E$ as shown below. The motion is
KVPY 2009, Advanced
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(c)
Given, potential energy curve closely represents potential energy of a simple harmonic oscillator $\left(U=\frac{1}{2} k x^2\right.$, shown in dotted line $)$
In region $r_1 < x < r_2$, the potential energy is less than total energy, so motion of particle in this region is oscillatory.
Also, the potential energy curve is not symmetric about $x=r_{\text {. }}$.
$\therefore$ Motion is not a simple harmonic.
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