Anharmonicity - General Principle

General Principle

A generalized version of harmonic oscillator in which the relationship between force and displacement is linear. The harmonic oscillator is a highly idealized system that oscillates with a single frequency, irrespective of the amount of pumping or energy injected into the system. Consequently, the harmonic oscillator's fundamental frequency of vibration is independent of the amplitude of the vibrations. Applications of the harmonic oscillator model abound in various fields, but perhaps the most commonly studied system is the Hooke's law mass-spring system. In the Hooke's law system the restoring force exerted on the mass is proportional to the displacement of the mass from its equilibrium position. This linear relationship between force and displacement mandates that the oscillation frequency of the mass will be independent of the amplitude of the displacement.

In a mechanical anharmonic oscillator, the relationship between force and displacement is not linear but depends upon the amplitude of the displacement. The nonlinearity arises from the fact that the spring is not capable of exerting a restoring force that is proportional to its displacement because of, for example, stretching in the material comprising the spring. As a result of the nonlinearity, the vibration frequency can change, depending upon the system's displacement. These changes in the vibration frequency result in energy being coupled from the fundamental vibration frequency to other frequencies through a process known as parametric coupling.