A block `(B)` is attached to two unstriched sprig `S_(1)` and S_(2) with spring constant `K` and `4K` , respectively (see fig 1) The other ends are atteched in identical support `M_(1)` and `M_(2)` not attached in the walls . The springs and supports have negligible mass . There is no friction anywhere . The block `B` is displaced toword wall `1` by a small distance `z` (figure (ii)) and released . THe block return and moves a maximum displacements `x` and `y` are musured with reoact to the equalibrum of the block `B` and the ratio `y//x` is

Options

A. 4
B. 2
C. `1//2`
D. `1//4`

Answer

C

Explanation

According to low of conservation of energy
`(1)/(2) k x^(2) = (1)/(2) ( 4k) y^(2) rArr (y)/( x) = sqrt((1)/( 4)) = (1)/(2)`