Resonance (Cambridge International A-Level Physics)

Spec point — 17.3.3

Resonance

• Resonance involves a maximum amplitude of oscillation that occurs when an oscillating system is forced to oscillate at its natural frequency

  • All oscillating systems have a natural frequency (f₀), the frequency at which the system is allowed to oscillate freely
  • The driving frequency (f) is the frequency of the forced oscillations

• When the driving frequency approaches the natural frequency of an oscillator, the system gains more energy from the driving force

  • Eventually, when they are equal, the oscillator vibrates with its maximum amplitude, this is resonance

• For example, when a child is pushed on a swing:

  • The swing and child have a fixed natural frequency
  • A small push after each cycle creates the driving frequency increasing the amplitude of the oscillations so the child swings higher
  • Resonance occurs when the driving frequency is equal to the natural frequency
  • When the driving frequency does not quite match the natural frequency, the amplitude will increase but not to the same extent as when resonance is achieved

• At resonance, energy is transferred from the driver to the oscillating system in the most efficient way

  • Therefore, at resonance, the system transfers the maximum kinetic energy possible

A child pushed on a swing

The person pushing the swing supplies an applied force to the system at the driving frequency until the child oscillates at the maximum frequency, the natural frequency