CoachPush an oscillator periodically — forced oscillations — and after a brief transient it oscillates at the driving frequency , not its own. Its amplitude peaks when nears the natural frequency of the free oscillator: this is resonance, each push arriving in step with the motion, feeding in energy every cycle; the lighter the damping, the taller and sharper the peak.
Examples
Example 28.14 (Resonance for good and ill)
A parent pushing a swing pushes at its own frequency — resonance put to work. In the new Millennium Bridge in London swayed alarmingly when the crowd’s steps locked onto a natural frequency near ; it closed two years for dampers. Every quartz watch keeps its crystal singing by driving it at resonance, .