5.2 - Damping and Resonance

Natural Frequency and Damping

Natural frequency is the frequency at which a displaced system oscillates freely without an external driving force.
Damping is a reduction in oscillation amplitude caused by loss of energy. The amplitude decreases with time until the oscillation stops.
The displacement–time graph has successively smaller peaks. The amplitude–time graph decreases with time; the oscillation frequency remains constant in the illustrated damped system.

Cause	Energy loss
External damping	Energy is used to overcome friction or air resistance.
Internal damping	Energy is lost through stretching and compression of vibrating particles within the system.

A simple pendulum experiences significant external damping and insignificant internal damping. Both are significant in a vibrating spring.
In the sugar-filled pendulum demonstration, the decreasing width of the deposited pattern represents decreasing amplitude.

A periodic force acts at specific time intervals rather than continuously.
A periodic external force supplies energy to replace energy lost through damping, producing a forced oscillation.
Resonance occurs when the frequency of the applied periodic force equals the system’s natural frequency. The system oscillates at its natural frequency with maximum amplitude.
Two tuning forks of the same frequency: striking fork P transfers energy to fork Q. Fork Q resonates and produces sound without being struck.
Barton’s pendulum: oscillations of the brass pendulum X transfer energy to the other pendulums. Pendulum C, with the same length and natural frequency as X, resonates with the largest amplitude.

Resonance is used when tuning musical instruments.
Strong winds caused large oscillations of Tacoma Narrows Bridge, which collapsed in 1940.
London Millennium Footbridge, opened in June 2000, experienced unexpected oscillations when about 2 000 pedestrians walked on it.