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A spring mass system is on a horizontal plane. Spring constant is 2N/m & mass of block is 2kg. The spring is compressed by 10cm and released. A small ball is released from a height of 2m above the block on the horizontal plane. At what time should the ball be left if the block is released from the extreme position at t=0, given that the ball has to fall on the block when the speed of block is maximum?

A spring mass system is on a horizontal plane. Spring constant is 2N/m & mass of block is 2kg. The spring is compressed by 10cm and released. A small ball is released from a height of 2m above the block on the horizontal plane. At what time should the ball be left if the block is released from the extreme position at t=0, given that the ball has to fall on the block when the speed of block is maximum? Correct Answer 0.94s

w = √2/2 = 1. Time period of SHM = 2π/w = 2π s. Speed of the block will be maximum at the mean position. Time to reach mean position from extreme position = T/4 = 2π/4 = π/2 =1.57s. Time for the small ball to fall down = √(2h/g) = √(4/9.8) = 0.63s. ∴ Time when it should be released = 1.57 – 0.63 s = 0.94s.

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