Question

A block $B$ is attached to two unstretched springs $S_1$ and $S_2$ with spring constants $k$ and $4k$ respectively (fig.(a)). 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 normal distance $x$ (fig. (b)) and released. The block returns and moves a maximum distance $y$ towards wall $2$. Displacement $x$ and $y$ are measured with respect to the equilibrium position of the block $B$. Find $y/x$ .

Answer 1

Energy stored in spring 1 in fig.b is $=\frac{1}{2}k{x}^2$

In figure (c) energy is stored in spring(2) only that is equal ti initial energy stored in spring 1.

$\frac{1}{2}\left(4k\right)y^2=\frac{1}{2}\times k{x}^2$

$(\frac{y}{x}{)}^2=\frac{1}{4}$

$\frac{y}{x}=\frac{1}{2}$