Forced Oscillator
Interactive simulation — adjust parameters and watch the visualization update in real time.
Live graphs
How it works
A damped harmonic oscillator driven by a sinusoidal force shows transient motion followed by steady oscillations at the drive frequency. The steady-state amplitude versus drive frequency peaks near the natural frequency ω₀ = √(k/m); damping broadens and lowers the peak. The analytic amplitude uses the standard harmonic-steady formula; numerical integration (RK2) shows the same long-time behavior after transients decay.
Key equations
mẍ + bẋ + kx = F₀ cos(ωt)
A = (F₀/m) / √((ω₀² − ω²)² + (bω/m)²) · ω₀² = k/m