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 `x` (figure (ii)) and released . The block return and moves a maximum distance y towards wall 2.Displacements x and y are measured w.r.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

From energy conservation, `1/2 kx^2 = 1/2 (4k) y^2 " " :. " " y/x = 1/2` .