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.

Options

A. At point 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 energy is k /2, it has its minimum kinetic energy at the origin
D. For small displacements from x = 0, the motion is simple harmonic

Answer

D