Serway & Jewett — Oscillatory Motion: Problem 22

Consider the physical pendulum of Figure 15.16. (a) Represent its moment of inertia about an axis passing through its center of mass and parallel to the axis passing through its pivot point as \(I_{CM}\). Show that its period is \[ T = 2\pi \sqrt{\frac{I_{CM} + md^2}{mgd}} \] where \(d\) is the distance between the pivot point and the center of mass. (b) Show that the period has a minimum value when \(d\) satisfies \(md^2 = I_{CM}\).