Past exam of the mathematical methods I course of the University of Oxford / 2017 resit / 7 / a / Solution

Hooke's law and Newton's second law give $m\ddot{x}=-kx$, so ${\omega }_0=\sqrt{k/m}$. The initial conditions select the simple harmonic motionThe kinetic energy and elastic potential energy exchange periodically while their sum $E_0=k{x}_0^2/2$ is constant.