There exist many methods of adding damping to a vibrating structure; however, eddy current damping is one of few that can function without ever coming into contact with that structure. This magnetic damping scheme functions due to the eddy currents that are generated in a conductive material when it is subjected to a time changing magnetic field. Due to the circulation of these currents, a magnetic field is generated, which interacts with the applied field resulting in a force. In this manuscript, an active damper will be theoretically developed that functions by dynamically modifying the current flowing through a coil, thus generating a time-varying magnetic field. By actively controlling the strength of the field around the conductor, the induced eddy currents and the resulting damping force can be controlled. This actuation method is easy to apply and allows significant magnitudes of forces to be applied without ever coming into contact with the structure. Therefore, vibration control can be applied without inducing mass loading or added stiffness, which are downfalls of other methods. This manuscript will provide a theoretical derivation of the equations defining the electric fields generated and the dynamic forces induced in the structure. This derivation will show that when eddy currents are generated due to a variation in the strength of the magnetic source, the resulting force occurs at twice the frequency of the applied current. This frequency doubling effect will be experimentally verified. Furthermore, a feedback controller will be designed to account for the frequency doubling effect and a simulation performed to show that significant vibration suppression can be achieved with this technique.