Question #42252

A uniform solid disc of mass $m = 2 \text{ kg}$ and radius $R = 0.5 \text{ m}$ is pivoted at a point on its edge. The pivot is attached to a straight torsional wire with a torsional constant $C = 7 \text{ N m rad}^{-1}$. The wire is perpendicular to the plane of the disc and serves as the axis of rotation. The setup is fixed such that the wire makes an angle of $30^\circ$ with the downward vertical. If the disc is given a small angular displacement in its own plane from its stable equilibrium position, what is the time period of the resulting simple harmonic motion? (Assume $g = 10 \text{ m s}^{-2}$)