The pendulum: A paradigm for the linear oscillator

Abstract

The simple pendulum is a model for the linear oscillator. The usual mathematical treatment of the problem begins with a differential equation that one solves with the techniques of the differential calculus, a formal process that tends to obscure the physics. In this paper we begin with a kinematic description of the motion obtained by experiment and a dynamic description obtained by the application of Newton's laws. We then impose the constraint of compatibility on the two descriptions. This method leads to a fuller understanding of the physics of the oscillator. The paper demonstrates the ubiquity of the linear oscillator as an idealisation of real physical phenomena. It treats the general case of damping with forced motion, including the phenomenon of resonance. © 2005 Springer.