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Anharmonic oscillation
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Real potentials deviate from parabolic at large amplitude.
Real potentials are not exactly parabolic; for larger amplitudes the period depends on amplitude and harmonics appear.
A pendulum at large angles, molecular vibrations.
Always examine whether SHM is valid.
In more detail
Anharmonic oscillators have restoring forces that are not proportional to displacement, so their period depends on amplitude. Real springs and atomic bonds are often anharmonic at large displacements.
Real-world uses
- Molecular bonds are anharmonic, which causes thermal expansion.
- Engineers account for anharmonic behaviour in large vibrations of structures.
- A real spring stretched far enough deviates from Hooke's law, which changes its period at large amplitude.
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Frequently asked questions
Why does anharmonicity matter?
It changes the frequency with amplitude, which can lead to distortion and harmonics.
Is SHM ever exact?
Only for an ideal harmonic restoring force, which is an approximation.
What is an anharmonic oscillator?
One where the restoring force is not exactly proportional to displacement, so the period depends on the amplitude.
Related topics in Oscillations & SHM
Beats in oscillators · Superposition of SHMs · Lissajous figures · Nonlinear oscillators · Chaos and the double pendulum · Parametric resonance