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This study uses a linear model of an Integrated Power and Attitude Control System (IPACS) to investigate the vibration interaction between multiple flywheels. An easily extendable Matlab script is created for the analysis of flywheel vibrations. This script is used to build a vibration model consisting of two active magnetic bearing flywheels mounted on a support structure. The flywheels are rotated at varying speeds, with an imbalance-induced centripetal force in one or both wheels causing vibrations in both wheels. Flywheel and system responses are examined for low frequency vibrations which would cause undesirable excitation to a satellite using IPACS, with a specific focus on the beat phenomenon and extra-synchronous vibration.