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 .