A block $(B)$ is attached to two unstretched $S_1$ and $S_2$ with spring constants $k$ and $4 k$,…
A block $(B)$ is attached to two unstretched $S_1$ and $S_2$ with spring constants $k$ and $4 k$, respectively (see figure I). The other ends are attached to identical supports $M_1$ and $M_2$ not attached to the walls. The springs and supports have negligible mass. There is no friction anywhere. The block $B$ is displaced towards wall 1 by a small distance $x$ (figure II) and released. The block returns and moves a maximum distance $y$ towards wall 2 . Displacements $x$ and $y$ are measured with respect to the equilibrium position of the block $B$. The ratio $\frac{y}{-1}$ is
4
2
$\frac{1}{2}$
$\frac{1}{4}$
Solution
From energy conservation,
$
\begin{aligned}
\frac{1}{2} k x^2 & =\frac{1}{2}(4 k) y^2 \\
\frac{y}{x} & =\frac{1}{2}
\end{aligned}
$
$\therefore$ correct option is (c)
