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Parametric resonance
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Oscillation driven by varying a parameter, like pumping a swing.
Varying a parameter (e.g., length) at twice the natural frequency pumps energy into the oscillator. A child pumping a swing by standing and crouching.
Used in parametric amplifiers.
Different from a driven force at ω₀.
In more detail
Parametric resonance occurs when a system's parameter, such as the length of a pendulum or the stiffness of a spring, is varied periodically at twice its natural frequency. The amplitude can grow rapidly.
Real-world uses
- Children pumping a swing change their posture to increase amplitude.
- Particle accelerators use parametric resonance to focus beams.
- A child on a swing raises and lowers their body at the right moments, which pumps energy into the motion without a push.
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Frequently asked questions
How is it different from forced resonance?
Here the driving force changes a parameter rather than acting as an external force.
Why twice the natural frequency?
Because the parameter variation must match the time it takes for the oscillation to repeat.
Is parametric resonance the same as forced resonance?
No. In parametric resonance, the system's parameter, such as the length, is varied, rather than a force being applied.
Related topics in Oscillations & SHM
Anharmonic oscillation · Nonlinear oscillators · Chaos and the double pendulum · Oscillation of a floating body · Liquid in a U-tube · Tunnel through the Earth