Consider given Problem again. This time find the motion of the particle by using the transformed energy equation.
Problem
A particle P of mass m can slide along a smooth rigid straight wire. The wire has one of its points fixed at the origin O, and is made to rotate in a plane through O with constant angular speed . Show that r, the distance of P from O, satisfies the equation
r·· - π2r = 0.
Initially, P is at rest (relative to the wire) at a distance a from O. Find r as a function of t in the subsequent motion.