A particle free to move along the \( x \)-axis has potential energy given by \( \mathrm{P} \) \[...
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0A particle free to move along the \( x \)-axis has potential energy given by
\( \mathrm{P} \)
\[
U(x)=k\left[1-\exp \left(-x^{2}\right)\right] \text { for }-\infty \leq x \leq+\infty
\]
W
where \( k \) is a constant of appropriate dimensions. Then :
(A) At points 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) If its total mechanical energy is \( k / 2 \), its has its minimum kinetic energy at the origin
(D) For small displacements from \( x=0 \), the motion is simple harmonic
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