A great challenge

Classical Mechanics Level pending

A ring of mass m can slide along a fixed rough vertical rod. The ring is connected by a spring of spring constant k = 4mg/R where 2R is the natural length of the spring . The other end of spring is fixed to the ground at point A at a horizontal distance of 2R from the base of the rod. If the ring is released from a height of 3R/2 and it reaches the ground with speed root over 3gR . Find coefficient of friction between rod and ring

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