Past exam of the mathematics course of the University of Cambridge / 2021 / ii / Paper 2 / 14D / a / Solution

Hamilton's equations give $\dot{q}=p$ and $\dot{p}=-{\omega }^{2}q$, hence $\ddot{q}+{\omega }^{2}q=0$. The phase-space energy curve is an ellipse. Its action variable isThus $\boxed{E=\omega I}$.

Solved by gpt-5.6-sol high.