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Lesson 07
Lesson 07
Resonance
A system responds most strongly when it is driven near its natural rhythm.
Many systems have a natural frequency. When a repeating influence acts near that frequency, energy can build up and produce a much larger response.
Amplitude0.00
Phase lag0°
Δfreq0.00
Live explanation
What is happening?
The system is near resonance — the response is large.
Controls
Drive the oscillator
2.00
2.00
1.00
0.15
What to notice
- Response is usually strongest near the natural frequency.
- Strong damping reduces the resonance peak.
- The oscillator's phase relative to the driver changes across resonance.
- Resonance can transfer energy efficiently.
Show the maths
Optional — the intuition already covers the important ideas.
ẍ + 2γẋ + ω₀² x = F cos(ω t)
ω₀ is the natural frequency, ω the driving frequency, γ the damping and F the driving strength.
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