The Comparative Experimental Study of Smartphone-Based Measurement Techniques for Simple Harmonic Motion

Abstract

Accurate experimental characterization of simple harmonic motion (SHM) is crucial for validating theoretical models and measurement methods. This study comparatively investigates three smartphone-based techniques, namely stroboscopic imaging, video tracking (Tracker software), and inertial sensor measurements (Phyphox app) applied to a vertical springmass system under identical conditions. Displacement time data were analyzed via nonlinear sinusoidal curve fitting and autocorrelation to determine oscillation periods, with theoretical predictions for both bare and mass-loaded configurations. A systematic uncertainty framework was implemented, accounting for temporal resolution, spatial calibration error, sensor noise, damping, and mass-loading corrections. Residual analysis indicated that deviations from ideal harmonic behavior were primarily due to instrumental resolution. The results show video tracking provides reliable quantitative measurements without perturbing system inertia, while inertial sensing yields consistent results when mechanical mass loading is modeled. Conversely, the stroboscopic method is limited by temporal discretization and manual analysis, restricting its use to qualitative visualization. These findings clarify the accuracy, limitations, and applicability of smartphone-based SHM measurements within a quantified experimental framework.