Question

A block $(B)$ is attached to two unstretched springs $S_{1}$ and $S_{2}$ with spring constants $k$ and $4 k$, respectively. The other ends are attached to two 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 $x$ 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

Answer: (C)

From energy conservation,
$\frac{1}{2} k x^{2} =\frac{1}{2}(4 k) y^{2}$
$\therefore \frac{y}{x} =\frac{1}{2}$