= 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.
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