Smartphone vision tracks nonlinear harmonics in vertical mass-spring oscillator beyond linear approximation

The setup records position at 30-60 Hz via OpenCV blob tracking on a phone clamped above the spring, exporting time series for immediate FFT and phase-space plots. Experiments demonstrate clear second-harmonic peaks when amplitude exceeds 15 percent of spring length, plus 1:2 frequency locking between vertical and pendulum modes once damping is reduced below 0.08 s inverse. Traditional photogate or ruler methods miss these because they sample too sparsely or assume small-angle linearity. The authors flag that camera lens distortion and lighting variance remain uncontrolled, limiting quantitative accuracy to roughly 3 percent displacement error.

Prior smartphone physics papers focused on linear period versus mass or damped decay; this work uniquely couples real-time visualization with nonlinear spectral signatures in a single vertical geometry. It therefore bridges the gap between textbook simple-harmonic motion and research-grade studies of energy transfer in weakly nonlinear oscillators. Because the apparatus costs under 50 USD and runs on existing phones, it lowers the barrier for institutions that cannot afford high-speed cameras or force sensors.

Next steps include releasing open-source code with automatic distortion correction and testing whether student groups can reproduce the reported 1:3 resonance tongue within a two-hour lab session. Controlled replication across multiple phone models would strengthen claims that the method is robust enough for widespread curriculum adoption.