The Pendulum: A Paradigm for the Linear Oscillator

The simple pendulum is a model for the linear oscillator. The usual mathematicaltreatment of the problem begins with a differential equation that one solves withthe techniques of the differential calculus, a formal process that tends to obscurethe physics. In this paper we begin with a kinematic description of the motionobtained by experiment and a dynamic description obtained by the applicationof Newton's laws. We then impose the constraint of compatibility on the twodescriptions. This method leads to a fuller understanding of the physics of theoscillator. The paper demonstrates the ubiquity of the linear oscillator as anidealisation of real physical phenomena. It treats the general case of dampingwith forced motion, including the phenomenon of resonance.