This thesis describes experiments performed on a system consisting of a superconducting tin disc suspended to oscillate about its axis as a torsion pendulum. This disc is made to oscillate in a uniform magnetic field directed normal to its surface. Some nonuniformity is introduced in the field by having the disc oscillate above and parallel to a superconducting tin plate of the same diameter as the disc. Regularly spaced holes drilled in the plate trapped flux which also penetrated the pendulum, producing intermediate-state regions. The resulting motion was damped harmonic motion with the damping torque proportional to the angular velocity. This was indicated by graphs of the logarithm of the amplitude against time giving straight lines. This was true for nonuniform fields produced by plates having many holes, few holes, or no holes. The conclusion was that the damping torque is proportional to the angular velocity regardless of how the nonuniformity in the field is produced. Damping in the normal state in a uniform field without any plate was explained as being due to a small horizontal component of the magnetic field which was due partly to the coils and partly to the earth's field.