When a particle of mass m moves on the x axis in a potential

Last updated: 6/10/2023

When a particle of mass m moves on the x axis in a potential of the form V z kz It performs simple harmonic motion The corresponding time period is proportional to 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 k2 and its total energy is such that the particle does not escape to infinitely Consider a particle of mass m moving on the x axis Its potential energy is V x ax a 0 for a near the origin and becomes a constant equal to Vo for lz X see figure If the total energy of the particle is E it will perform periodic motion only if m V x A M