CIE A Level Physics (9702) exams from 2022

Revision Notes

17.2.2 Resonance


  • In order to sustain oscillations in a simple harmonic system, a periodic force must be applied to replace the energy lost in damping
    • This periodic force does work on the resistive force decreasing the oscillations
  • These are known as forced oscillations, and are defined as:

Periodic forces which are applied in order to sustain oscillations

  • For example, when a child is on a swing, they will be pushed at one end after each cycle in order to keep swinging and prevent air resistance from damping the oscillations
    • These extra pushes are the forced oscillations, without them, the child will eventually come to a stop
  • The frequency of forced oscillations is referred to as the driving frequency (f)
  • All oscillating systems have a natural frequency (f0), this is defined as:

The frequency of an oscillation when the oscillating system is allowed to oscillate freely

  • Oscillating systems can exhibit a property known as resonance
  • When resonance is achieved, a maximum amplitude of oscillations can be observed
  • Resonance is defined as:

When the driving frequency applied to an oscillating system is equal to its natural frequency, the amplitude of the resulting oscillations increases significantly

  • For example, when a child is pushed on a swing:
    • The swing plus the child has a fixed natural frequency
    • A small push after each cycle increases the amplitude of the oscillations to swing the child higher
    • If the driving frequency does not quite match the natural frequency, the amplitude will increase but not to the same extent at when resonance is achieved
  • This is because at resonance, energy is transferred from the driver to the oscillating system most efficiently
    • Therefore, at resonance, the system will be transferring the maximum kinetic energy possible
  • A graph of driving frequency f against amplitude a of oscillations is called a resonance curve. It has the following key features:
    • When f < f0, the amplitude of oscillations increases
    • At the peak where f = f0, the amplitude is at its maximum. This is resonance
    • When f > f0, the amplitude of oscillations starts to decrease
  • Damping reduces the amplitude of resonance vibrations
  • The height and shape of the resonance curve will therefore change slightly depending on the degree of damping
    • Note: the natural frequency f0 will remain the same
  • As the degree of damping is increased, the resonance graph is altered in the following ways:
    • The amplitude of resonance vibrations decrease, meaning the peak of the curve lowers
    • The resonance peak broadens
    • The resonance peak moves slightly to the left of the natural frequency when heavily damped

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