Question

The potential energy of a particle oscillating on x-axis is given as U = 20 + (x - 2)². Here, U is in joules and x in metre . Total mechanical energy of the particle is 36 J.

(a) State whether the motion of the particle is simple harmonic or not

(b) Find the mean position,

(c) Find the maximum kinetic energy of the particle.

Answer 1

(a)

By assuming x - 2 = X we have

The motion of the particle is simple harmonic 

(b) The mean position of the particle is X  = 0 or x - 2 = 0, which give x = 2 m

(c) Maximum kinetic energy of the particle is,