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Question

One end of a spring of force constant k is fixed to a vertical wall and the other end is connected to a block of mass m resting on a smooth horizontal surface. There is another wall at a distance x0 from the body. The spring is now compressed by 3x0 and released. The time after which the block will strike the other wall is
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A
11π9mk
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B
2π3mk
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C
π4mk
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D
π6mk
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Solution

The correct option is B 2π3mk
Amplitude of the motion,A=2×0
We know that the time needed to cover from compressed
position to mean position =T4
For the displacement from the mean position to
XO time taken t will be
Y=Asinwt
XO=2XOsinwt
but w=2πT
or,XO=2XOsin2πTt
or,12=sin2πTt
or,2πTt=sin(0.5)2πTt=π6t=T12
Time taken to hit the wall=T4+T12=T3
If mass M is suspended from he spring of force constant
k,T=2πMR
Time taken to hit the wall =T3=2π3MR
Hence option B is correct answer.

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