In the figure shown, a spring mass system is placed on a horizontal smooth surface in between two vertical rigid walls `W_(1)` and `W_(2)`. One end of spring is fixed with wall `W_(1)` and other end is attached with mass `m` which is free to move. Initially, spring is tension free and having natural length `l_(0)`. Mass `m` is compressed through a distance a and released. Taking the collision between wall `W_(2)` and mass `m` as elastic and `K` as spring constant, the average force exerted by mass `m` on wall `W_(2)` in one oscillation of block is

Options

A. `(2aK)/(pi)`
B. `(2ma)/(pi)`
C. `(aK)/(pi)`
D. `(2aK)/(m)`

Answer

A

Explanation

`v_(max) = omega A = (sqrt((K)/(m)))a`
`DeltaP = 2m v(max) = 2m(sqrt(K)/(m))a`
`F = (Delta P)/(Delta t) = (Delta P)/(T//2) = (2ma sqrt (k//m))/(pi sqrt (m//k)) = (2aK)/(pi)`