C.4.4—Resonance

Separate the frequencies

The natural frequency is the frequency at which a system oscillates after a disturbance when it is left alone. The driving frequency is imposed by an external periodic force. Resonance occurs when the driving frequency is equal or very close to the system’s natural frequency, producing a large amplitude response.

Explain the large amplitude

At resonance, the driving force supplies energy efficiently to the oscillator each cycle because its timing is well matched to the motion. The amplitude rises until the energy supplied per cycle is balanced by energy dissipated. Greater energy dissipation means a smaller maximum amplitude.

Read a frequency-response graph

Plot amplitude against driving frequency. The peak identifies the resonant frequency; the peak height is the maximum amplitude. A practical system may have its peak slightly displaced from its undamped natural frequency when damping is significant, but the syllabus requires only a qualitative frequency-response analysis.

Recognize useful and destructive resonance

Resonance is useful when a large, frequency-selective response is wanted, such as tuning a receiver or producing a strong musical sound. It can be destructive when repeated driving builds damaging oscillations in a bridge, building or machine. Designs then change the natural frequency, avoid the matching driving frequency, or add damping.

Common trap

Do not call the driving frequency the natural frequency. A large amplitude alone is not enough to establish resonance: connect it to the driving frequency being close to the natural frequency and to efficient energy transfer.