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\includegraphics[max width=\textwidth, alt={}, center]{b86c4b97-13a9-4aaf-8c95-20fe043b4532-2_653_406_727_857} A lamina has mass 1.5 kg . Two perpendicular lines \(A B\) and \(C D\) in the lamina intersect at the point \(X\). The centre of mass, \(G\), of the lamina lies on \(A B\), and \(X G = 0.2 \mathrm {~m}\) (see diagram). The moment of inertia of the lamina about \(A B\) is \(0.02 \mathrm {~kg} \mathrm {~m} ^ { 2 }\), and the moment of inertia of the lamina about \(C D\) is \(0.12 \mathrm {~kg} \mathrm {~m} ^ { 2 }\). The lamina is free to rotate in a vertical plane about a fixed horizontal axis perpendicular to the lamina and passing through \(X\).

1. The lamina makes small oscillations as a compound pendulum. Find the approximate period of these oscillations.
2. The lamina starts at rest with \(G\) vertically below \(X\). A couple of constant moment 3.2 Nm about the axis is now applied to the lamina. Find the angular speed of the lamina when \(X G\) is first horizontal.