Damped Mass–Spring Analytics for H2 Physics Practical Excellence

TL;DR
A tripod-mounted smartphone filming a spring–mass oscillation gives you displacement–time data you can digitise in Tracker or PhyPhox.
Fit an exponential decay to determine damping coefficients, compare with theory, and practise writing uncertainty paragraphs on gradients, intercepts, and logarithmic decrement.
The workflow reinforces SHM theory while meeting SEAB's digital-data expectations for 2026 Paper 4.

Why Add Damping to Your Practical Portfolio

• Examiner reports repeatedly flag weak candidate commentary on non-ideal oscillations; this investigation fixes that blind spot.
• Quantifying damping ties directly to Wave & SHM chapters in the 9478 syllabus and expands beyond the typical simple pendulum write-up.
• Smartphones + free apps reduce hardware costs while delivering the high data density Cambridge praises in top scripts.

Apparatus Checklist

Experimental Procedure

1. Calibrate the scale. Stick a 10 mm grid behind the mass. Record a calibration frame for Tracker to convert pixels to metres.
2. Capture the motion. Pull the mass down ~2 cm, release without sideways kick, and record for at least 20 oscillations at 60 fps.
3. Digitise data. Track the mass position frame-by-frame. Export displacement vs time to CSV.
4. Analyse with spreadsheets. Fit x(t) = A e^{-\gamma t} \cos(\omega_d t + \phi) using nonlinear regression or generate a semi-log plot of successive peak amplitudes.
5. Compute logarithmic decrement \delta = \ln\left(\frac{x_n}{x_{n+1}}\right) and damping ratio \zeta = \frac{\delta}{\sqrt{4\pi^2 + \delta^2}}.
6. Estimate uncertainties. Use LINEST to obtain standard errors and propagate video tracking resolution into \delta and \zeta.

Examiner-Level Discussion Points

• Energy dissipation. Link the exponential envelope to energy loss per cycle and encourage students to quantify the fractional energy loss.
• Critical damping comparison. Swap in a viscous damper to approach \zeta = 1 and discuss why shocks absorbers target \zeta \approx 0.7.
• Frequency shift. Highlight how damped frequency \omega_d = \omega_0\sqrt{1-\zeta^2} deviates from the natural frequency and validate with your data.
• Uncertainty narrative. Comment on dominant sources — camera perspective, calibration grid measurement, and time-base jitter — and suggest mitigations.

Differentiation and CTA Ideas

• Offer a weekend “Oscillations Data Studio” class where students bring their CSVs and practise curve fitting with Python or Desmos.
• Cross-link to Video Analysis of Projectile Motion to reinforce video-based measurement skills.
• Provide an optional PASCO or Vernier motion sensor dataset for comparison so students can evaluate smartphone vs lab-grade equipment.

References

• PhET Interactive Simulations, Masses and Springs
• Barba, L. et al., A low-cost damped oscillator lab using smartphones, arXiv:2004.01436
• Singapore Examinations and Assessment Board, GCE A-Level Examinations practical requirements