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Damped oscillations
Intermediate
Friction gradually reduces amplitude.
x = Ae^{−bt/2m}cos(ω't)With damping force −bv the amplitude decays as e^{−bt/2m}. The frequency ω' = √(ω₀² − (b/2m)²) is slightly lower than the natural frequency.
A swing coming gradually to rest.
The envelope decays exponentially, not linearly.
In more detail
Damping is the loss of energy from an oscillator, usually by friction or drag. The amplitude decays exponentially with time, and the system eventually comes to rest.
Real-world uses
- Shock absorbers in cars damp oscillations after bumps.
- Door closers are damped to close doors smoothly.
- A car's shock absorbers damp its oscillations so that the ride settles quickly after a bump.
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Frequently asked questions
Why does damping matter?
It controls how quickly oscillations die out, which affects comfort and safety.
Does damping change the period?
Slightly, for light damping, the frequency is reduced compared with the undamped value.
Does damping change the period?
Slightly. The damped frequency is a little lower than the natural frequency, and the amplitude decays over time.
Related topics in Oscillations & SHM
Kinetic and potential energy in SHM · Average energy over a cycle · Differential equation of SHM · Underdamped, critical, overdamped · Quality factor · Forced oscillations