Problem 1

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 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 $B$ . Find the ratio $\dfrac yx$ .

This is a problem of Energy Tranfers .