Wobbly ellipse

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

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


The answer is 4.3303.

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