$A$ $1\, kg$ block moves towards a light spring with a velocity of $8\, m/s$. When the spring is compressed by $3\, m$,its momentum becomes half of the original momentum. The spring constant of the spring is:

An elastic string of unstretched length $L$ and force constant $k$ is stretched by a small length $x$. It is further stretched by another small length $y$. The work done in the second stretching is

$A$ block $B$ is attached to two unstretched springs $S1$ and $S2$ with spring constants $k$ and $4k$,respectively (see figure $I$). The other ends are attached to identical supports $M1$ and $M2$ which are 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:

An engine is attached to a wagon through a shock absorber of length $1.5 \, m$. The system with a total mass of $50,000 \, kg$ is moving with a speed of $36 \, km \, h^{-1}$ when the brakes are applied to bring it to rest. In the process of the system being brought to rest,the spring of the shock absorber gets compressed by $1.0 \, m$. If $90 \%$ of the energy of the wagon is lost due to friction,calculate the spring constant.

$A$ spring with spring constant $k$ is extended from $x = 0$ to $x = x_1$. The work done will be

$A$ block of mass $m$ moving with speed $v$ compresses a spring through distance $x$ before its speed is halved. What is the value of the spring constant $k$?