Question

An L-shaped bar of mass M is pivoted at one of its end so that it can freely rotate in a vertical plane, as shown in the figure.

(a) Find the value of θ₀ at equilibrium.

(b) If it is slightly displaced from its equilibrium position, find the frequency of oscillation.

Answer 1

(a) Taking B as the origin, the co-ordinates of its c.m. are

(b) The frequency of oscillation for a compound pendulum is

where d = distance of the COM from the point of suspension. I = moment of inertia about the point of suspension.