Question

Assertion: In a S.H.M., kinetic and potential energies become equal when the displacement is 1/√2 times the amplitude. Reason: In SHM, kinetic energy is zero when potential energy is maximum

A particle of mass m is attached to a spring and performs linear simple harmonic motion with amplitude A and angular frequency ω. (a) Derive the expression for the total mechanical energy of the particle and state whether it depends on time. (b) Draw neat, labelled graphs to show the variation of kinetic energy and potential energy of the particle with time during one complete oscillation. (c) It is observed that both K.E. and P.E. repeat twice in one oscillation. Justify this observation with reference to the frequency of kinetic and potential energies compared to the frequency of the particle.