Concept# Harmonic oscillator

Summary

In classical mechanics, a harmonic oscillator is a system that, when displaced from its equilibrium position, experiences a restoring force F proportional to the displacement x:
\vec F = -k \vec x,
where k is a positive constant.
If F is the only force acting on the system, the system is called a simple harmonic oscillator, and it undergoes simple harmonic motion: sinusoidal oscillations about the equilibrium point, with a constant amplitude and a constant frequency (which does not depend on the amplitude).
If a frictional force (damping) proportional to the velocity is also present, the harmonic oscillator is described as a damped oscillator. Depending on the friction coefficient, the system can:

- Oscillate with a frequency lower than in the undamped case, and an amplitude decreasing with time (underdamped oscillator).
- Decay to the equilibrium position, without oscillations (overdamped oscillator).

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