Introduction

Harmonic motion is periodic motion where the displacement of an object as a function of time can be expressed in terms of a sum of sines and cosines. Simple harmonic motion (SHM) refers to a special case of harmonic motion where the magnitude of the restoring force (F) acting on an object is directly proportional to its displacement (x) from an equilibrium position:

SHM is one of the most common types of motion found in nature with examples being water waves, sound waves, vibrating springs and pendulums.

A spring force has the form of equation (1), where x is the displacement of the end of the spring (and mass) from its equilibrium position and k is a proportionality constant called a spring constant.