Halliday, Resnick & Walker — Oscillations: Problem Problem_55

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 m and its mass is m = 22.1 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?