Halliday, Resnick & Walker — Oscillations: Problem 10

10 In Fig. 15-25a, a metal plate is mounted on an axle through its center of mass. A spring with \(k = 3600 \text{ N/m}\) connects a wall with a point on the rim a distance \(r = 3.0 \text{ cm}\) from the center of mass. Initially the spring is at its rest length. If the plate is rotated by \(7^\circ\) and released, it rotates about the axle in SHM, with its angular position given by Fig. 15-25b. The horizontal axis scale is set by \(t_s = 30 \text{ ms}\). What is the rotational inertia of the plate about its center of mass?