Forced Oscillator

This interactive simulator explores Forced Oscillator in Classical Mechanics. Driven damped harmonic oscillator: transients, resonance curve A(ω). 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: Best once you already know the basic definitions and want to build intuition. Typical context: Classical Mechanics.

Key terms

  • forced
  • oscillator
  • forced oscillator
  • mechanics
  • classical

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