UC Santa Cruz

In this paper we study a phenomena observed in the seventeenth century by Christiaan Huygens. He found that two pendulum clocks placed on a common support synchronized over time. We study a model of this type of coupling primarily using the fourth-order Runge-Kutta method. We look at time series to get a picture of what types of synchronization occur and then once we figure out how to classify synchronization we study how varying the damping in the system affects the synchronization. We next look at what happens when driven pendulums replace the clocks. We compare phase portraits and bifurcation diagrams of the uncoupled driven pendulum to the coupled driven pendulums to get a picture of how the dynamics and chaotic tendencies of the driven pendulum change with the coupling.