Damped harmonic oscillator

A system that oscillates while dissipating energy, causing its amplitude to decrease over time. Its motion depends on the balance between restoring force, inertia, and damping.

Damping ratio: A dimensionless measure comparing a system’s damping with the damping that produces critical decay. It classifies the oscillator’s response as underdamped, critically damped, or overdamped.
Simple harmonic motion: Periodic motion in which the restoring force is proportional to displacement and directed toward equilibrium. Removing dissipation from this motion gives the undamped oscillator.
Shock absorber: A device that dissipates energy from suspension motion to reduce vehicle bouncing. It uses damping to suppress oscillations after a bump.
Undamped harmonic oscillator: An ideal oscillator that undergoes harmonic motion without losing energy to its surroundings. It keeps constant amplitude, unlike the dissipative system considered here.
Underdamping: A regime in which a damped system continues oscillating as its amplitude decays. This is the oscillatory regime of the damped harmonic oscillator.
Hooke's law: The relation stating that an elastic force is proportional to displacement from equilibrium within a material’s elastic range. A linear restoring force produces the oscillator’s characteristic harmonic response.
Seismometer: An instrument that measures ground motion, often using a suspended mass relative to its frame. Its moving mass is designed and calibrated as a damped mechanical oscillator.
Driven harmonic oscillator: An oscillator subject to an external periodic force, which can sustain or amplify its motion. External forcing distinguishes its steady response from free decay.
Critical damping: The threshold damping that returns a system to equilibrium as quickly as possible without oscillation. It marks the boundary between oscillatory and nonoscillatory decay.
Viscous damping: Energy dissipation produced by a resistive force proportional to velocity. It supplies the standard linear damping term in the oscillator equation.

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