Paragraph: When a particle of mass m moves on the x -axis in a potential of the form V(x)=k x^2 , it performs simple harmonic motion. The corresponding time period is proportional to m k , as can be seen easily using dimensional analysis. However, the motion of a particle can be periodic even when its potential energy increases on both sides of x=0 in a way different from k x^2 and its total energy is such that the p