Damped & Driven Oscillation Lab
Set mass, spring constant, and damping coefficient, then watch real-time oscillation. Switch to driven mode to sweep driving frequency and discover resonance peaks, phase lag, and the role of the quality factor Q.
Guided ExperimentObserving Damping Regimes
How will the motion differ when the damping ratio ζ is less than 1, equal to 1, and greater than 1? Which regime returns the system to equilibrium fastest?
Write your hypothesis in the Lab Report panel, then click Next.
Mass-Spring-Damper System
Displacement vs Time
Controls
Results
Data Table
(0 rows)| # | Trial | Mode | ω_d(rad/s) | Amplitude(cm) | Phase Lag(°) | Q Factor | ζ | Classification |
|---|
Reference Guide
Free Damped Oscillation
A mass on a spring with damping follows the equation of motion
The natural angular frequency is and the damping ratio is .
When (underdamped), the system oscillates with exponentially decaying amplitude. When (critically damped), it returns to zero fastest without overshoot. When (overdamped), it returns slowly without oscillating.
Driven Oscillation and Resonance
When an external periodic force is applied, the equation becomes
After transients decay, the steady-state amplitude is
The amplitude peaks near the natural frequency. The resonance frequency is (valid when ).
Quality Factor Q
The quality factor measures how underdamped the system is
A high Q means the system rings for many cycles before damping out. At resonance, the peak amplitude is approximately
The width of the resonance peak (half-power bandwidth) is inversely proportional to Q.
Phase Lag
The response of a driven oscillator lags behind the driving force by a phase angle
At low frequency the displacement is nearly in phase with the force (φ near 0). At resonance the phase lag is 90°. Well above resonance the displacement is nearly 180° out of phase, meaning the mass moves opposite to the applied force.
