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This paper focuses on a class of robot manipulators termed "continuum" robots - robots that exhibit behavior similar to tentacles, trunks, and snakes. In previous work, we studied details of the mechanical design, kinematics, path-planning and small-deflection dynamics for continuum robots such as the Clemson "tentacle manipulator". In this paper, we discuss the dynamics of a planar continuum backbone section, incorporating a large-deflection dynamic model. Based on these dynamics, we formulate a vibration-damping setpoint controller, and include experimental results to illustrate the efficacy of the proposed controller.