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A particle free to move along the X-axis...

A particle free to move along the `X-`axis has potential energy given by `U(X)=k[1-exp(-X^(2))]` of appropriate dimensions. Then-

A

at point away from the origin, the particle is in unstable equilibrium

B

for any finite nonzero value of `X`, there is a force directed away from the origin

C

it its total mechanical energy is `k//2`, it has its minimum kinetic energy at the origin

D

for small displacement from `X=0`, the motion is simple harmonic

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The correct Answer is:
D
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