A block $(B)$ is attached to two unstretched springs $\mathrm{S} 1$ and $\mathrm{S} 2$ with spring constants $\mathrm{k}$ and $4 \mathrm{k}$, respectively (see figure $\mathrm{I}$ ). The other ends are attached to identical supports $M1$ and $M2$ not attached to the walls. The springs and supports have negligible mass. There is no friction anywhere. The block $\mathrm{B}$ is displaced towards wall $1$ by a small distance $\mathrm{x}$ (figure $II$) and released. The block returns and moves a maximum distance $\mathrm{y}$ towards wall $2$ . Displacements $\mathrm{x}$ and $\mathrm{y}$ are measured with respect to the equilibrium position of the block $B$. The ratio $\frac{y}{x}$ is Figure: $Image$

Two identical blocks $A$ and $B$ each of mass $m$ resting on the smooth horizontal floor are connected by a light spring of natural length $L$ and spring constant $K$. A third block $C$ of mass $m$ moving with a speed $v$ along the line joining $A$ and $B$ collides with $A$.The maximum compression in the spring is

The spring extends by $x$ on loading, then energy stored by the spring is :(if $T$ is the tension in spring and $k$ is spring constant)

A ring of mass $m$ is attached to a horizontal spring of spring constant $k$ and natural length $l_0$ . Other end of spring is fixed and ring can slide on a smooth horizontal rod as shown. Now the ring is shifted to position $B$ and released, speed of ring when spring attains it's natural length is

A body of mass $ 0.1 kg $ moving with a velocity of $10 m/s$  hits a spring (fixed at the other end) of force constant $ 1000 N/m $ and comes to rest after compressing the spring. The compression of the spring is .............. $\mathrm{m}$

$A$ block of mass $m$ moving with a velocity $v_0$ on a smooth horizontal surface strikes and compresses a spring of stiffness $k$ till mass comes to rest as shown in the figure. This phenomenon is observed by two observers:

$A$: standing on the horizontal surface

$B$: standing on the block 

To an observer $A$, the work done by spring force is