Halliday, Resnick & Walker — Oscillations: Problem 47

47 A pendulum is formed by pivoting a long thin rod about a point on the rod. In a series of experiments, the period is measured as a function of the distance \(x\) between the pivot point and the rod’s center. (a) If the rod’s length is \(L = 2.20\text{ m}\) and its mass is \(m = 20.5\text{ g}\), what is the minimum period? (b) If \(x\) is chosen to minimize the period and then \(L\) is increased, does the period increase, decrease, or remain the same? (c) If, instead, \(m\) is increased without \(L\) increasing, does the period increase, decrease, or remain the same?