Past exam of the physics course of the year 4 of the natural sciences course of the University of Cambridge / 2013 / Paper 1 / Section B / B1 / a / Solution

At $r_0=6L/5$, the frequency ratio is $\Omega /{\omega }_0=3$. There are three radial oscillations during one mean revolution, giving a nearly circular orbit with three outward and three inward extrema. The leading small-amplitude sketch closes after one revolution. Finite-amplitude corrections generally change the frequency ratio and can produce apsidal drift; the linear ratio does not prove an exactly closed finite-amplitude orbit for the full stretched-string potential.