Exact and Approximate Formulae for the Period of Simple Pendulum

Abstract

Pendulum plays a significant role in certain practical aspects such as measuring gravitational acceleration and proving the rotation of Earth. In traditional textbooks, only a simplified approximate formula for calculating pendulum period in small angle is given. As a matter of fact, the analytical derivation of the pendulum period can always be given in the form of elliptical integral simply using the law of the conservation of energy. The form, however, is relatively complex for students and beginners in physics. Thus, a simplified version of the period of simple pendulum is highly desirable. This article is going to present a series of approximate formulae for pendulum period and conduct some comparison among these different formulae. This essay is dedicated to help readers and beginners in physics to look into the process of deriving the pendulum period formula, and also provide a convenient way for readers to look up certain literatures in this research area.