Damped driven oscillator
To push a swing well you have to find the rhythm — that's resonance.
A damped oscillator driven by a periodic force oscillates at the driving frequency in the steady state. Its amplitude depends on the driving frequency: near the natural frequency the amplitude rises sharply, which is resonance. The smaller the damping, the higher and sharper the resonance peak and the larger the quality factor Q = 1/(2ζ). The displacement lags the driving force by a phase δ: δ = 90° at resonance, approaching 180° far above the natural frequency.
Resonance curve: amplitude vs. driving frequency
The smaller the damping, the higher and narrower the peak; the peak lies at ω/ω₀ = √(1 − 2ζ²).
Think about it
At resonance, what is the phase difference between the oscillator's displacement and the driving force?
90°. Set the frequency ratio to 1 and watch the blue response arrow in the phasor diagram stay a quarter turn behind the green driving arrow.
Model assumptionsLinear spring, viscous damping · steady state only · natural frequency 1 Hz · static displacement 1 cm
Data log
Set the parameters and click “Record data”. Record several rows with different parameters to plot their relationship and fit a straight line; pause and record at different times to study how a reading changes with time.