A particle is attached to a fixed point O on a smooth horizontal plane by an elastic string. When unstretched, the length of the string is 2a. The equation of motion of the particle, which is...

A particle is attached to a fixed point O on a smooth horizontal plane by an elastic string. When unstretched, the length of the string is 2a. The equation of motion of the particle, which is constrained to move on a straight line through 0, is

x being the displacement from 0. Find the equilibrium points and the equations of the phase paths, and sketch the phase diagram.