Question

A mass is undergoing SHM in the vertical direction about the mean position with amplitude A and angular frequency . At a distance from the mean position, the mass detaches from the spring. Assume that the spring contracts and does not obstruct the motion of . Find the distance (measured from the mean position) such that the height attained by the block is maximum.

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A

B

C

D

None of these

Hard
Updated on : 2022-09-05
Solution
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Correct option is A)

Let    be the upward velocity of the block when it detaches from the spring at a distance above the mean position.
      ..........(1)
At the detaching point, the block will continue to move upwards due to inertia and reach the  height   above the mean position. At that height the velocity of the block will be zero.
Thus        
Now the total height    
For    to be maximum,    
Thus      

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