Past exam of the mathematical methods II course of the University of Oxford / 2014 resit / 8 / a

Measure each rod angle from the downward vertical, as in the held diagram. The upper mass rises by $2l(1-\cos {\theta }_1)$; the lower mass rises by $2l(1-\cos {\theta }_1)+l(1-\cos {\theta }_2)$. With the hanging equilibrium as the zero of gravitational potential energy,The retained expression is quadratic in the small displacements. Both masses contribute to the upper rod's gravitational term.