Theoretical and experimental study of the motion of the simple pendulum

Abstract

A pedagogic experimental and theoretical study of the motion of the simple pendulum, which considers corrections to the approximation of simple harmonic motion, is presented. The period is calculated with the use of both elliptic integrals and the perturbation theory of Kryloff and Bogoliuboff. Measurements of the period of the pendulum taken with a stopwatch are compared with the calculations. The errors made in the measurements are analyzed.