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Resonance
Intermediate
Large amplitude when driving frequency matches natural frequency.
ω_d ≈ ω₀When ω_d ≈ ω₀, amplitude peaks and energy transfers efficiently. The peak height is limited by damping.
Radio tuner selects a station by resonance.
Can cause destructive effects.
In more detail
Resonance occurs when a driving frequency equals the natural frequency of an oscillator, giving the largest amplitude. Damping limits how large the amplitude becomes.
Real-world uses
- Tuning a radio uses resonance to select one station.
- Musical instruments amplify sound at their resonant frequencies.
- Radio tuning circuits and musical instruments exploit resonance, where a small driving force builds up a large response.
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Frequently asked questions
Is resonance dangerous?
It can be, if a structure is driven at its natural frequency, as in the Tacoma Narrows failure.
What limits the amplitude?
Damping, since energy is removed each cycle.
Why does resonance make a big amplitude?
The driving force keeps adding energy in phase with the motion, so the amplitude grows until damping balances the input.
Related topics in Oscillations & SHM
Underdamped, critical, overdamped · Quality factor · Forced oscillations · Resonance examples · Amplitude vs frequency curve · LC oscillations