Complex systems for high school physics: synchronization using low-cost experiments and the Kuramoto model

Abstract This work presents a pedagogical approach for introducing synchronization phenomena in high school physics education through the Kuramoto model, contributing to complex systems education at the secondary level. Synchronization occurs when coupled oscillators, initially out of phase, begin to oscillate in phase with a common frequency due to coupling between their constituent elements. This phenomenon is widely observed in nature and artificial systems, from firefly flashing patterns to mechanical metronomes, yet remains largely absent from secondary education curricula. We propose a two-stage methodology to make this complex concept accessible to high school students. The first stage involves experimental investigation using video analysis with Tracker software to study coupled metronomes, allowing students to observe phase relationships and measure synchronization dynamics. The second stage utilizes computational simulations to explore the mathematical framework of the Kuramoto model and examine various coupling scenarios. This approach bridges the gap between advanced physics concepts typically reserved for university-level courses and secondary education, enabling educators to effectively teach sophisticated phenomena from complex systems at the high school level. The methodology integrates theoretical understanding with hands-on experimentation and computational modelling, providing students with multiple perspectives on synchronization phenomena.