SHM Question No. 15 November 2014 Examination.

[himanshu]

A particle undergoes simple harmonic motion of maximum kinetic energy Emax and amplitude xo. The particle is release from rest at its maximum displace amplitude. What is the change in the kinetic energy when the particle has traveled a distance of xo /3?

[kw0573]

In SHM, potential energy E_p = 1/2 * kx². Because initially all energy is potential, E_max = 1/2 * k * x₀², When the particle travel a distance of x₀ / 3, the displacement from equilibrium position is now 2x₀ / 3, which lead to a potential energy of 1/2 * k * (2x₀ / 3)² = 4/9 * 1/2 * k * x₀² = 4/9 E_max. 

By conservation of energy, the remaining energy exists in form of kinetic energy, so E_k = E_max - 4/9 E_max = 5/9 E_max = change in kinetic energy because initial kinetic energy was 0.