The motion of a copper plate is damped when it is allowed to oscillate between the two poles of a magnet. What is the cause of this damping?

As the copper plate oscillates in the magnetic field between the two poles of the magnet, there is a continuous change of magnetic field, flux linked with the pendulum. Due to this, eddy currents are set up in the copper plate which try to oppose the motion of the pendulum according to Lenz's law and finally bring it to rest.