Force on a particle is given by: F = -kxn. For what values of n will the motion be oscillatory?(k is a positive constant)

For motion to be oscillatory there has to be an equilibrium position towards which the force is acting throughout the motion. In the expression, F = -kxn,If n is even, force will always act in one direction.If n is odd, force will change direction when x changes direction and will always act towards the origin.Hence, motion will be oscillatory if n is odd.Thus, from the given options 3 is correct.