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We focus on a class of robotic manipulators that utilize continuous backbone structures. Such manipulators, known as "continuum" robots, exhibit behavior similar to tentacles, trunks, and snakes. Specifically, we have previously discussed some of the mechanical and kinematic details of the Clemson -Tentacle Manipulator." This work examines the dynamic characteristics of this manipulator, proposing a vibration damping control strategy for configurations with the worst vibration characteristics. We begin by formulating the dynamics for one section of the Tentacle Manipulator. We then proceed to develop a vibration control strategy which incorporates a setpoint regulator. We supplement the theoretical developments with experimental results.