The dynamic behavior of conducting mechanical structures in high magnetic fields is complicated by the currents and forces induced by motion through the magnetic field. A series of experiments that were successfully conducted to investigate the coupling between induced currents and rigid body rotation in square loops and plates is presented. The experiments were performed with the Fusion Electromagnetic Induction Experiment facility at the Argonne National Laboratory. The observed data exhibited the magnetic damping and magnetic stiffness effects that arise in coupled systems and agreed very well with the predicted responses for both the loops and plates. The experimental arrangement consisted of a conducting test piece, rigidly mounted in a nonconducting fixture that provided a controlled stiffness against rotation. Electric currents were induced in the test loop/plate by pulsing a magnetic field oriented perpendicular to the test piece. This was done in the presence of a constant magnetic field oriented parallel to the loop/plate. The interaction of the induced currents and the background magnetic field produced a net torque about the axis of the test fixture. Measurements were made of the total current flowing around the test piece and the angular rotation versus time.