Damped Driven Oscillation
Explore m*xddot+b*xdot+k*x=F0*cos(omega*t), distinguishing a transient trajectory from steady-state amplitude and damping-dependent displacement resonance.
Free theory articleExplore m*xddot+b*xdot+k*x=F0*cos(omega*t), distinguishing a transient trajectory from steady-state amplitude and damping-dependent displacement resonance.
Concept & interpretation
A damped driven oscillator extends simple harmonic motion by adding a resistive damping force proportional to velocity and a periodic external driving force. The equation of motion ism · x″ + b · x′ + k · x = F₀ · cos(ω · t). For positive damping, the free transient decays and the motion approaches a forced response at the driving frequency. With zero damping the free motion persists; at exact resonance the driven motion grows without a bounded steady state.
Interactive Experiment
You can reproduce this behavior using the Damped Driven Oscillation module:
- Set Mass (m) to 1.0 kg and Stiffness (k) to 4.0 N/m.
- Set Damping (b) to 1.0 kg/s.
- Set Drive Force (F₀) to 1.0 N and Drive Freq (ω) to 2.0 rad/s.
- Click Step for fixed 0.1-second updates or Play for continuous motion. Observe the initial transient motion which eventually decays.
- Notice that the steady-state oscillation amplitude stabilizes near 0.5 m. The view fits the displacement automatically; pixel length is not a fixed physical scale.