For a conducting material exposed to both a time-varying and a static magnetic field, such as a limiter blade in a tokamak, the induced eddy currents and the deflection arising from those eddy currents can be strongly coupled. The coupling effects reduce the currents and deflections markedly, sometimes an order of magnitude, from the values predicted if coupling is neglected. A series of experiments conceived by researchers at the Princeton Plasma Physics Laboratory to study current-deflection coupling were performed using the Fusion Electromagnetic Inductance Experiment (FELIX) facility at Argonne National Laboratory. Magnetic damping and magnetic stiffness resulting from the coupling are discussed, and analytical expressions for induced eddy currents and rigid body rotation in the FELIX plate experiment are compared with the experimental results. Predictions for the degree of coupling based on various parameters are made using the analytical model.