Resonance

Shake a spring at its natural frequency and watch the amplitude climb.

0/2challenges

t = 0.0 s

Drive (static displacement)Mass

Drive frequency ωrad/s

Drive force F₀N

Masskg

Stiffness kN/m

Damping cN·s/m

Natural frequency ω₀: 6.32rad/s
Quality factor Q: 10.5
Steady amplitude: 26.1cm
Measured now: 0.0cm
Phase lag: 11°

The model

A mass on a spring with a damper, shaken at the top: m x″ + c x′ + k x = F₀ cos ωt, integrated with RK4. After the start-up transient dies away, it oscillates at the drive frequency with a steady amplitude.

Near the natural frequency ω₀ = √(k/m) the amplitude peaks. The quality factor Q = √(mk) / c sets how tall and narrow the peak is: high Q means a sharp resonance and a long ring.

Try this

Set the drive just below ω₀ with light damping and watch the amplitude climb over many cycles. This is how wine glasses break and why bridges have dampers. Then raise the damping until the peak flattens out.

Linear spring, viscous damping and a sinusoidal drive; real springs stiffen and break. Educational model, not an engineering design or validation tool.

Achievements0/2

Resonance +30Drive the oscillator to ten times its static displacement.
Damper +20Keep the resonance peak under twice the static displacement.

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