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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[l-e^(-x^(2))]` for `-inftylexle+infty`, where k is positive constant of appropriate dimensions. Then:

A

at points away from the origin, the particle is in unstable equilibrium.

B

for any finite non-zero value of `x`, there is a force directed away from the origin

C

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

D

for small displacements from `x = 0`, the motion is simple harmonic.

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The correct Answer is:
A, B, C
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