A block (B) is attached to two unstretched springs $S_{1}$ 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 $\frac{y}{x}$ is [image:14_image2.png]

Question

Dr. Abubacker · Accepted Answer

(c) [image:14_image53.emf]
As springs and supports ($M_{1}$ and $M_{2}$) are having negligible mass. Whenever springs pull the massless supports, springs will be in natural length. At maximum compression, velocity of $B$ will be zero
[image:14_image54.emf]
And by energy conservation
$\frac{1}{2}(4K)y^{2} = \frac{1}{2}Kx^{2} \Rightarrow \frac{y}{x} = \frac{1}{2}$

Explanation

Reviewed by Dr. Abubacker

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