3\\
\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 $X$.\\
(i) The lamina makes small oscillations as a compound pendulum. Find the approximate period of these oscillations.\\
(ii) 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.

\hfill \mbox{\textit{OCR M4 2005 Q3 [7]}}