Duffing Oscillator
This interactive simulator explores Duffing Oscillator in Waves & Sound. m x¨+cx˙+kx+k₃x³=F cos ωt; soft/hard spring; A(ω) scan vs IC. Use the controls to change the scenario; watch the visualization and any graphs or readouts to connect the model with lectures, labs, and homework.
Who it's for: For learners comfortable with heavier math or second-level detail. Typical context: Waves & Sound.
Key terms
- duffing
- oscillator
- duffing oscillator
- waves
- sound
Live graphs
How it works
The **Duffing** model adds a cubic stiffness **k₃x³** to a damped, harmonically driven oscillator. **Softening** (k₃ < 0) bends the resonance peak toward lower frequencies; **hardening** (k₃ > 0) shifts it upward. Amplitude can be **multivalued** for the same drive frequency depending on initial conditions — a toy version is shown by comparing two numerical A(ω) sweeps. For large drive and damping, dynamics can become chaotic (not the focus here).
Key equations
More from Waves & Sound
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