Suppose the North pole of the magnet m be vertically below the South pole which on top. Magnetic field B due to m is directed outward from North pole. Vertically downwards and passing though the ring. The magnetic flux through the ring r is the product of field B and area A of the ring.
As the magnet m nears the ring, the flux through ring increases, as B increases continuously. An emf is induced in the ring r. To oppose the increase in FLux, the current flows in the ring in the anti clock wise direction when viewed from the top. This induced current has a magnetic field B' vertically upwards. Thus B' repels the North pole N of magnet m more than it attracts South pole S of m.
The repelling force acts opposite to the weight M g of the magnet. So the magnet accelerates downwards at a rate less than g.
Similarly, When the magnet has gone through the ring past it, the magnetic flux starts decreasing as B reduces continuously. Due to the Faraday's induction law, we have an emf induced in the ring to increase the flux.
So the current in the ring flows in the clockwise direction to add to the magnetic field strength B of magnet m. Now this magnetic field B' attracts South pole S which is nearer, more than the North pole.
Thus again the magnet travels down with an acceleration less than g.