The emergence of various patterns of synchronization within systems of
coupled self-sustained oscillators is a phenomenon which can be traced back
to Huygens’ clock experiments of 1665 [1]. Such occurrences can be found
on scales ranging from the subatomic to the cosmic and can arise as a result
of many different types of communication, including chemical, gravitational,
electrical, and mechanical. Despite recently capturing the attention of the
scientific community, the so-called ‘science of sync’ continues to evade perfect
understanding, particularly in the cases of vast oscillator networks for which
the exact connectivity of the system is unknown. This project investigated
the phenomenon of synchronization through the observation and analysis of
two unique dynamical systems, one mechanical and the other electronic. The
mechanical system consisted of two metronomes coupled by their shared use of
a rolling platform resting on two cylinders of equal radii, as initially presented
in [2, 3]. The dynamics of this system, including its steady final states and
symmetry-breaking transients, were experimentally studied using frame-by-frame
motion tracking software. Subsequent analysis of the platform’s movements
revealed the presence of Coulomb damping, and the original theoretical model
was reconstructed to take this into account. Additionally, each synchronization
region was classified in terms of both the coupling strength of the system and
the natural frequency mismatch between the two oscillators. Similar parameters
were examined for the electronic system, namely, two coupled comparator-based
relaxation oscillators (CBROs). Various phase-locked ratios, including 1:1,
2:1, 3:1, and 4:1, were experimentally measured and portrayed in the form of
Arnold tongues. These observed parameter regimes were then shown to almost
perfectly match the predictions of the system’s theoretical model.
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