Halliday, Resnick & Walker — Oscillations: Problem Problem_54

In Fig. 15.30a, a metal plate is mounted on an axle through its center of mass. A spring with k = 2000 N/m connects a wall with a point on the rim a distance r = 2.5 cm from the center of mass. Initially the spring is at its rest length. If the plate is rotated by 7° and released, it rotates about the axle in SHM, with its angular position given by Fig. 15.30b. The horizontal axis scale is set by \(t_s = 20 \text{ ms}\). What is the rotational inertia of the plate about its center of mass?