Theory and Numerics of Two Synchronized Oscillators

Author: Grau, Matthew Charles

Year: 2009

Degree: Senior thesis (Major)

Advisor: Cross, Michael Clifford

Committee Member: None, None

Option: Physics

DOI: 10.7907/8GXA-0M35

Abstract

Coupled oscillators are used to model systems such as arrays of lasers or detectors whose response is combined to increase signal strength. I investigated a systems of two coupled oscillators using a model incorporating features such as reactive (non-dissipative) force couplings and amplitude-dependent frequencies. I employed careful numerical simulations to build up intuition about the various behaviors of the model and then studied the model analytically to determine regions of synchronization, a phenomenon in which many oscillators lock their relative phase or frequency to a common equilibrium value. The result of this investigation can be used to motivate the choice of parameter values (such as spread of intrinsic frequencies or coupling strength) of small systems of nanomechanical oscillators currently being designed by Matt Matheny in the Roukes laboratory at Caltech.

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