Resonance
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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
