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Question

A block of mass m compresses a spring of stiffness k through a distance l/2 as shown in the figure. If the block is not fixed to the spring and released from this position, the period of motion of the block is


A

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B

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C

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D

(3+π)mk

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Solution

The correct option is B


The period of oscillation =2πmk

The period of motion till the block is in contact with the spring is

t=T2=πmk then it leaves the spring with a speed v=ωA

v=(km)(l2)

Then it moves with constant velocity v for a distance D=l+l=2l

The corresponding time of motion =t2=2lv

t2=2ll2km=4mk

The time period of motion =t=t1+t2

=πmk+4mk=mk[π+4]

the correct option is B.


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