Limits of the simple pendulum formula for classroom use

Abstract

Abstract We discuss the limits of the equation of the period of a simple pendulum, T s = 2 π l / g , frequently used in high-school and university classrooms to measure the acceleration of gravity. We evaluate the relative error in determining the acceleration of gravity with this simple equation instead of a more realistic one, taking into account the string’s mass, the bob’s radius, and finite angular displacements. We show that the bob radius and finite angular displacements increase the period of oscillation of the pendulum and, hence, contribute to a positive deviation in the value of g calculated with the simple pendulum formula. On the other hand, the string’s mass decreases the pendulum’s period and induces a negative deviation in the value of g. As a result, it is possible to adapt the pendulum’s characteristics to use the simple pendulum formula and calculate g with accuracy.