Anharmonic

In classical mechanics, anharmonicity is the deviation of a system from being a harmonic oscillator. An oscillator that is not oscillating in simple harmonic motion is known as an anharmonic oscillator where the system can be approximated to a harmonic oscillator and the anharmonicity can be calculated using perturbation theory. If the anharmonicity is large, then other numerical techniques have to be used.

As a result, oscillations with frequencies ${\displaystyle 2\omega }$ and ${\displaystyle 3\omega }$ etc., where ${\displaystyle \omega }$ is the fundamental frequency of the oscillator, appear. Furthermore, the frequency ${\displaystyle \omega }$ deviates from the frequency ${\displaystyle \omega _{0}}$ of the harmonic oscillations. As a first approximation, the frequency shift ${\displaystyle \Delta \omega =\omega -\omega _{0}}$ is proportional to the square of the oscillation amplitude ${\displaystyle A}$:

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