The magnet is attached to the spring. This magnet will execute simple harmonic motion. When a coil is placed in such a way that magnet moves in and out of the coil, an emf is induced in the coil which opposes the movement of magnet in the coil. Due to this induced emf galvanometer will show deflections to the left and right periodically.
As the emf is induced in the coil eddy currents are also induced in the magnet, which lowers down the total magnetic strength of the magnet. Due to this reason, the magnetic flux linked with the coil decrease and hence amplitude of the deflections produced in the galvanometer also decreases.