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

When block B is moved toward wall 1 then springs `S_(2)` (4K) remains in its normal length and spring `S_(1)` is compressed. Similarly, when block B cross the equilibrium on opposite side then only spring `S_(2)` is compressed and spring `S_(1)` remains in its neutral length. We can apply conservation of mechnical energy.
`(1)/(2)kx^(2) = (1)/(2)(4K)y^(2)`
`rArr (y)/(x) = (1)/(2)`