Resonance Amplitude vs. Driving Frequency
About This Graph
This interactive visualization shows the resonance curve - how the amplitude of a driven oscillator depends on the driving frequency. The dramatic peak at the resonance frequency (ωd = ω₀) demonstrates why small periodic forces can produce large oscillations.
Understanding the Graph
X-Axis: Frequency Ratio (ωd/ω₀)
- ωd/ω₀ < 1: Driving frequency below natural frequency
- ωd/ω₀ = 1: Resonance - driving matches natural frequency
- ωd/ω₀ > 1: Driving frequency above natural frequency
Y-Axis: Amplitude Ratio (A/A₀)
- Normalized amplitude compared to static displacement
- Can reach very high values at resonance with low damping
Effect of Damping
| Damping Level | Peak Height | Peak Width | Real Examples |
|---|---|---|---|
| Low (ζ < 0.3) | Very tall | Narrow | Tuning forks, guitar strings |
| Medium (ζ ≈ 0.5) | Moderate | Medium | Building structures |
| Critical (ζ = 1) | Low | Very broad | Shock absorbers |
| High (ζ > 1) | Minimal | No distinct peak | Heavy oil dampers |
Key Observations
- At resonance: Maximum energy transfer from driver to oscillator
- Below resonance: Motion follows driving force
- Above resonance: Motion opposes driving force (180° out of phase)
- Damping controls the peak: More damping = lower, broader peak
Lesson Plan
Discussion Questions
- Why do engineers need to know the natural frequency of structures?
- How does damping protect against destructive resonance?
- What happens if you push a swing at double its natural frequency?