Magnet dropping through a loop

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A permanent magnet of mass m is located on the vertical axis of a stationary, conducting , non-magnetic ring for a long time. The ring has a radius a, resistance R and inductance L.At time t=0 the magnet is released. Suppose the magnet has dipole moment \muz. Write down the equation of motion.

Is the retarding force due magnetic flux generated by the induced current passing through the loop? If that is the case how do I evaluate the equation of motion of the magnet?
 
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Consider Lenz' Law. Energy must be conserved, so the work done to create the current in the loop must equal the thermal energy generated in the loop.
 
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To solve this, I first used the units to work out that a= m* a/m, i.e. t=z/λ. This would allow you to determine the time duration within an interval section by section and then add this to the previous ones to obtain the age of the respective layer. However, this would require a constant thickness per year for each interval. However, since this is most likely not the case, my next consideration was that the age must be the integral of a 1/λ(z) function, which I cannot model.
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