Synchronization and Energy Transfer in Coupled Oscillators: Influence of Coupling, Damping, and Frequency

Coupled oscillators provide a simple framework for examining how interaction and dissipation modify collective dynamics and energy redistribution. This work jointly analyzes synchronization and energy transfer in two damped linear oscillators with close natural frequencies. A dimensionless model was formulated and a parametric sweep of coupling, damping, and frequency detuning was performed, including validation against analytical limits and an independent numerical solution. The results show that stronger coupling and near-resonant conditions favor energy transfer, whereas damping limits it. Nevertheless, high phase coherence does not necessarily imply efficient energy transfer. The separation between these behaviors shows that coupled systems should be characterized using complementary indicators and provides a reproducible basis for extensions to electrical, nonlinear, and vibrational systems.