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. (a) `4`
B. (b) `2`
C. (c) `1/2`
D. (d) `1/4`

Answer

C

Explanation

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