A spring has a natural length 
with one end fixed to the ceiling. The other end is fitted with a smooth ring which can slide on a horizontal rod fixed at distance 
below the ceiling.Initially, the spring makes an angle of 
with the vertical, when system is released from test. Find the angle of the spring with the vertical, when, the velocity of the ring reaches half of the maximum velocity, which the ring can attain during the motion.
Text Solution
Verified by ExpertsD
From diagram,
Extension in spring 
At mean position, if velocity is 
and there is no friction, then
If angle with vertical is 
when velocity is 
Then, 
Substituting value of 
, we have
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