Why oscillations die away
Damping occurs when resistive forces remove energy from an oscillating system, causing its amplitude to become progressively smaller.
Friction and air resistance act against the oscillator's motion. Work done against these forces transfers energy away from the oscillation.
If that lost energy is not replaced, the motion eventually dies away and the system settles at equilibrium.
A resistive force is different from a restoring force. The restoring force is directed towards equilibrium and produces the oscillation, whereas the resistive force opposes the velocity and reduces the oscillator's energy.
Degrees of damping
Light damping
The system continues to oscillate while successive amplitudes become smaller.
The envelope of the oscillation follows an exponential decay.
Successive peaks remain equally spaced, so the period and frequency stay unchanged as the amplitude falls.
Critical damping
The system does not pass repeatedly through equilibrium.
It settles at equilibrium as quickly as possible without overshooting and oscillating about it.
Heavy damping
The system also approaches equilibrium without oscillating about it.
Its approach is slower than in the critically damped case.
| Damping | Oscillates? | Behaviour | Typical example |
|---|---|---|---|
| Light | Yes | Oscillations gradually die away | A freely swinging pendulum losing amplitude |
| Critical | No | Settles most rapidly without overshooting | Car suspension designed to settle rapidly |
| Heavy | No | Approaches equilibrium more slowly | A strongly damped door closer |
Worked example: A mechanical scale has a pointer that oscillates around its final reading before settling. Which type of damping would make the reading available quickly without repeated oscillations?
With light damping, the pointer would continue moving back and forth before settling.
Heavy damping would stop repeated oscillations, but the pointer would take longer to reach its final position.
Critical damping lets the pointer settle rapidly without repeatedly crossing its final reading.
Therefore, critical damping is the most suitable.
Exam Tip: If asked to distinguish damping from the restoring effect, describe the force directions: a resistive force opposes the oscillator's velocity, whereas a restoring force is directed towards equilibrium.