Past exam of the mathematics course of the University of Cambridge / 2026 / ii / Paper 2 / 8A / b / Solution

The equilibria are $\theta =0,\pi$ modulo $2\pi$ unless $a=g$, when every angle is an equilibrium. Linearisation shows $heta=0$ stable for $a<g$ and $\theta =\pi$ stable for $a>g$; the other is unstable.