Pendulum Tracker -- SimuFísica: A Web-based Tool for Real-time Measurement of Oscillatory Motion

TL;DR

The paper tackles the need for real-time, accessible pendulum experiments in education by introducing Pendulum Tracker, a browser-based computer-vision tool built on OpenCV.js and integrated into the SimuFísica platform to measure angular motion and derive time-series data, periods, and gravity estimates in real time. It validates the approach through three application examples—period measurement, gravity determination, and damped oscillations—showing close agreement with theoretical predictions within experimental uncertainty, exemplified by the relation $T = 2\pi \sqrt{L/g}$. The work highlights the system's portability, immediate visualization, data export capabilities, and potential for offline deployment, making it a practical and scalable resource for physics pedagogy. All data are openly available, reinforcing transparency and enabling replication and further exploration in educational settings.

Abstract

We present Pendulum Tracker, a computer vision-based application that enables real-time measurement of the oscillatory motion of a physical pendulum. Integrated into the educational platform SimuFísica, the system uses the OpenCV.js library and runs directly in the browser, working on computers, tablets, and smartphones. The application automatically detects the pendulum's position via the device's camera, displaying in real time the angle-versus-time graph and estimates of the oscillation period. Experimental case studies demonstrate its effectiveness in measuring the period, determining gravitational acceleration, and analyzing damped oscillations. The results show excellent agreement with theoretical predictions, confirming the system's accuracy and its applicability in educational contexts. The accessible interface and the ability to export raw data make Pendulum Tracker a versatile tool for experimental physics teaching.

Figures (5)

• Figure 1: Pendulum Tracker application from the SimuFísica® platform. Access link: https://simufisica.com/en/pendulum-tracker/.
• Figure 2: Measurements performed using the Pendulum Tracker -- SimuFísica application with $L = 45.8 \pm 0.1$ cm.
• Figure 3: Results from the measurements shown in Fig. \ref{['fig2']}. (a) Angle as a function of time. (b) Zoom of (a) within a 4.7 s window. The line is a guide to the eye. (c) Green line shows the Fourier transform of (a), considering a 60 s interval. The black line is a Gaussian fit of the Fourier transform.
• Figure 4: Pendulum oscillation period as a function of length. (a) Linear scale: experimental data in blue and theoretical curve in red. (b) Log-log plot of the experimental data (blue) with linear fit (black line).
• Figure 5: (a) Damped oscillations of a simple pendulum. Experimental data in blue and theoretical curve in red. (b) Zoom of (a) up to $t = 7$ s. (c) Zoom of (a) in the time window $t \in [120, 127]$ s.