• 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 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. This 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

Resonance Effects

• Resonance occurs for any forced oscillation where the frequency of the driving force is equal to the natural frequency of the oscillator
• Examples include:
  • An organ pipe, where air resonates down an air column setting up a stationary wave in the pipe
  • Glass smashing from a high pitched sound wave at the right frequency
  • A radio tuned so that the electric circuit resonates at the same frequency as the specific broadcast

Standing waves forming inside an organ pipe from resonance