Resonance
When a system is driven at its natural oscillation frequency, the amplitude of its response grows much larger than it would at any other driving frequency.
Practise this conceptEvery system that can oscillate has a natural frequency — the rate it "wants" to vibrate at if left alone. Drive it with a periodic force at any other frequency, and it responds, but not very enthusiastically. Drive it at exactly its natural frequency, and the response grows dramatically larger: resonance.
A child on a swing demonstrates this perfectly. Small, well-timed pushes delivered at the swing's own natural rhythm build up amplitude far more than the same-sized pushes delivered at random or mismatched timing — it isn't the size of each push that matters most, it's the timing.
Resonance isn't limited to swings and musical instruments; it matters at every scale, including ones large enough to be dangerous. A famous example is the Tacoma Narrows Bridge, where wind-driven oscillations built up near one of the structure's natural frequencies until the amplitude became large enough to tear the bridge apart — a reminder that resonance can amplify a small, steady input into a very large effect.
Key ideas
Requires: Simple harmonic motion
Formulas
| Symbol | Name | Unit |
|---|---|---|
| frequency | Hz (hertz) | |
| stiffness | N/m (newton per metre) | |
| mass | kg (kilogram) |
Common misconceptions
- Resonance occurs at any driving frequency, not just the system's natural frequency.
- A larger driving force always produces a larger resonance effect, regardless of frequency.
- Resonance is dangerous only for large structures like bridges, never for small objects.