Question

A block (B) is attached to two unstretched springs $S_1$ and $S_2$ with spring constants $k$ and $4k$, 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 the wall 1 by a small distance $x$ 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 $\frac{y}{x}$ is:

• A. $4$
• B. $2$
• C. $\frac{1}{2}$
• D. $\frac{1}{4}$

Answer 1

The correct option is C $\frac{1}{2}$

From conservation of energy,

$\begin{array}{c}\frac{1}{2}k{x}^2=\frac{1}{2}\times 4k\times y^2\\ x^2=4y^2\\ x=2y\\ \frac{y}{x}=\frac{1}{2}\end{array}$