A particle of mass m executes simple harmonic motion with amplitude 'a' and frequency v. The average kinetic energy during its motion from theposition of equilibrium to the end is

The kinetic energy is given byK.E.=12mω2a2sin2⁡ωtThe average kinetic energy during its motion from the position of equilibrium to the end is given by(K.E.)Average =∫0T/4 12mω2a2sin2⁡ωtdt =π2ma2v2 (∵ω=2πv)