What is spring constant ? On which the work done by a spring depends ?

Two blocks of mass $2\ kg$ and $1\ kg$ are connected by an ideal spring on a rough surface. The spring in unstreched. Spring constant is $8\ N/m$ . Coefficient of friction is  $μ = 0.8$ . Now block $2\ kg$ is imparted a velocity $u$ towards $1\ kg$ block. Find the maximum value of velocity $'u'$ of block $2\ kg$ such that block of $1\ kg$ mass never move is

Two springs $A$ and $B$ having spring constant $K_{A}$ and $K_{B}\left(K_{A}=2 K_{B}\right)$ are stretched by applying force of equal magnitude. If energy stored in spring $A$ is $E_{A}$ then energy stored in $B$ will be

$A$ 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 

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

Two blocks $A(5kg)$ and  $B(2kg)$ attached to the ends of a spring constant $1120N/m$ are placed on a smooth horizontal plane with the spring undeformed. Simultaneously velocities of $3m/s$ and $10m/s$ along the line of the spring in the same direction are imparted to $A$ and $B$ then