A particle free to move along the x-axis has potential energy given by U(x) = K [1-exp(-x)2] for – ∞<–x<–+∞, where k is a positive constant of appropriate dimensions. Then
(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
(7)