A block of mass m compresses a spring iof stifffness k through a distacne `l//2` as shown in the figure .If the block is not fixed to the spring the period of motion of the block is

Options

A. `2pisqrt(m/k)`
B. `(pi+4)sqrt(m/k)`
C. `(1+pi)sqrt(m/k)`
D. None of these

Answer

2

Explanation

The period of a oscillation of string till block is in contact with the spring is `t_(1) =pisqrt(m/K)`
then it leaves the contact with spring with velocity
`V= Aomega = (l)/(2) sqrt(K/m)`
"Now is will move with constant velocity v for a distane D= l+l =2l"
"the corresponding time for motion"
`t_(2)=(2l)/(v)=(2l)/(l/2)sqrt(k/m)=4sqrt(m/k)`
"So the total time" `t=t_(1)+t_(2) =pisqrt(m/K)+4sqrt(m/K)`
`=(pi+4)sqrt(m/K)`