Coupled oscillations

The harmonic oscillator, and the more complicated systems for which it stands as a simple model, has a single degree of freedom. More complicated systems have more degrees of freedom, for example two masses and two springs. In such cases, energy is converted between the respective inertias of each degree of freedom and the several restoring forces in the system. This leads to a coupling of the oscillations of the individual degrees of freedom. For example, two pendulum clocks mounted on a common wall will tend to synchronise. The apparent motions of the individual oscillations typically appears very complicated but a more economic, computationally simpler and conceptually deeper description is given by resolving the motion into normal modes