A thin superconducting ring is held above a vertical, cylindrical magnetic rod. The axis of symmetry of the ring is the same as that of the rod. The cylindrically symmetrical magnetic field around the ring can be described approximately in terms of vertical and radial components of magnetic field vectorwhereare positive constants, z and r are vertical and radial position coordinates respectively. Initially ring has no current flowing in it. When released it starts to move downwards with its axis still vertical and it performs harmonic oscillations for small displacement. Initially z = 0 for ring. Mass of the ring is m, radius is r and its inductance is L.

Ring makes harmonic oscillations with amplitude: