Forced oscillations and resonance – driven spring–mass system
PhysicsOscillations & WavesAges 16–17Virtual lab
Use it with your class: students open it from a link or a QR code, with no account needed.
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A horizontal spring–mass system is driven by a vibrator that applies a periodic force F = F₀cos(2πft). Students see the transient stage and then steady oscillation at the driving frequency f, and sweep f back and forth to build the resonance curve A(f), which peaks at the natural frequency f₀. Change the damping to see a sharp or broad resonance peak; switch off the driving force to see damped oscillations.
Lesson: Damped and forced oscillations, resonance
What it shows
A spring–mass system driven by a periodic force first passes through a transient stage and then settles into steady oscillation at the driving frequency f, not at its own natural frequency f₀ = (1/2π)√(k/m). The steady amplitude depends on how close f is to f₀: plotting amplitude against f gives a resonance curve that peaks near f₀. Damping, modelled as a force proportional to velocity, limits the height of the peak and widens the curve. Without the driving force, the oscillation dies away inside an exponential envelope A₀e^(−bt/2m).
How to use
With light damping, move the f slider in small steps from below f₀ to above it. After each change wait for the steady state; with Auto-record when steady ticked, each amplitude is added to the resonance curve, or press Record A(f). A higher Speed setting saves time. Tick Theoretical curve to compare, then repeat with moderate and heavy damping. Finally press Driver off to watch the damped oscillation decay.
Parameters you can change
- Spring constant 10–100 N/m
- Mass 0.1–1 kg
- Damping Light (b = 0.2 kg/s), Moderate (b = 0.5 kg/s), Heavy (b = 1.2 kg/s)
- Driving force amplitude F₀ 0.02–0.2 N
- Initial driving frequency 0.2–3 Hz
- Driving force on (off: damped oscillation)
Questions to explore
- In the steady state, does the mass oscillate at its natural frequency or at the driving frequency? How can you tell?
- How does heavier damping change the maximum amplitude and the width of the resonance curve?
- After the driver is switched off with light damping, how long does the amplitude take to fall to about 37% of its value?
