Resonance (CIE A Level Physics)

• The frequency of forced oscillations is referred to as the driving frequency (f) or the frequency of the applied force
• All oscillating systems have a natural frequency (f₀), this is defined as this is the frequency of an oscillation when the oscillating system is allowed to oscillate freely

• Oscillating systems can exhibit a property known as resonance
• 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

• Resonance is defined as:

When the frequency of the applied force 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. The frequency at which this push happens is the driving frequency
  • When the driving frequency is exactly equal to the natural frequency of the swing oscillations, resonance occurs
  • If 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

• 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 Child Being 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 

Resonance Curve

• 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

The Resonance Curve

The maximum amplitude of the oscillations occurs when the driving frequency is equal to the natural frequency of the oscillator