(a) Starting from the expressions for kinetic and potential energies of a mass–spring system, prove that the total mechanical energy is equal to the maximum kinetic energy.
(b) Hence obtain an expression for the total energy solely in terms of the mass m and the maximum speed vmax.
(c) A body of mass 0.25kg oscillates such that its maximum speed is 0.50ms−1. Calculate the total mechanical energy of the system using the result from part (b).