The concept of a harmonic oscillator is very familiar to us.  Imagine a clock with a pendulum swinging back and forth.  The pendulum is undergoing harmonic motion - that is, it is undergoing a motion that repeats itself with a characteristic time period.  In the case of the pendulum, it is the time required for the pendulum to complete one full swing.  There are numerous other examples of harmonic motion in the physical world - both at the every day and microscopic scales.  The theory of the harmonic oscillator is therefore of great importance, and an introduction to the theory of the harmonic oscillator is presented in these articles.

In the first article, the simplest form of harmonic motion, termed simple harmonic motion, is discussed.  In addition, some everyday examples of simple harmonic motion are presented.  The second article considers some of the important results about the energy of a simple harmonic oscillator, in particular the interplay between the kinetic and potential energies of a harmonic oscillator.  The third and fourth articles cover extensions of the simple harmonic oscillator, namely the damped oscillator and the forced oscillator.  The fifth article discusses how anharmonic (non-linear) effects can be taken into account in the context of the simple pendulum, and the final article considers a slightly more complex oscillating system, the triatomic molecule.

Note that the words and interpretation here are my own.  I have made no attempt at a rigorous treatment, and as such have neglected many aspects of the subject.  I have discussed the parts of the theory that interest me, and my aim is only to give a flavour of the harmonic oscillator, and what it is all about. 

Simple Harmonic Oscillator

Energy Considerations

Damped harmonic Motion

Forced Harmonic Motion and Resonance

The Simple Pendulum

The Importance of the harmonic Oscillator