Question

A block (5) is attached to two unstretched springs $S_1 \, \, and \, \, S_2$ with spring constants k and 4k, 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)

$\frac{1}{2}$

Answer 2

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