A particle is executing linear SHM. The average kinetic energy and average potential energy, over a period of oscillation, respectively are Kav and Uav. Then,

K = 12mv2 = 12mA2ω2cos2ωtAverage value of cos2 ωt is 12 over one cycle∴  Kav = 14mω2A2------------(i)      U = 12mω2x2 = 12mω2A2sin2ωtAverage value of sin2 ωt is 12 over one cycle.∴  Uav = 14mω2A2 ---------(iii)From Eqs. (i) and (ii), we get Kav = Uav