Wobbly ellipse

Consider an elliptical lamina with semi-minor axis \(b = 1 \text{ m}\) and eccentricity \(e = 0.5\) kept vertically on a table-top. Find the time period \(T\) (in S.I. units) of small oscillations about its stable equilibrium position.

Take \(g = 10\text{ ms}^{-1} \).

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