Let $O$ be a fixed point of the body and suppose that $O, \underline{e_1},\underline{e_2}, \underline{e_3}$ form principal axes for the body with principal moments of inertia $A, B, C $. The body is free to rotate about the point $O$ about the axis $\underline{e_3}$ which are both fixed. The $\underline{e_3}$ axis is horizontal. Suppose that the centre of mass lies a distance $h$ along the positive $\underline{e_1}$ axis and let $\theta$ denote the angle between $\underline{e_1}$ and the downward vertical.
Deduce that, $$\ddot{\theta} = -\frac{Mgh}{C}sin{\theta}.$$
Using an appropriate approximation solve this equation for a small $\theta$.
Obviously a set shape is needed in order to find out the moment f inertia values for $A, B, C$. So i am unsure how to tackle this question without those.
Any ideas?