A particle free to move along the (x - axis) hsd potential energy given by `U(x)= k[1 - exp(-x^2)] for -o o le x le + o o`, where (k) is a 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.
