Question

A thin uniform plate shaped as an equilateral triangle with a height h performs small oscillations about the horizontal axis coinciding with one of its sides. Find the oscillation period and the reduced length of the given pendulum.

Answer 1

Consider the moment of inertia of the triangular plate AB.

On using the area of the triangle

Here θ is the angle that the instantaneous plane of the plate makes with the equilibrium position which is vertical is vertical. (The plate rotates as a rigid body)