A block is fastened to a horizontal spring. The block is pulled to a distance $x =10\,cm$ from its equilibrium position (at $x =0$ ) on a frictionless surface from rest. The energy of the block at $x =5$ $cm$ is $0.25\,J$. The spring constant of the spring is $.........Nm ^{-1}$

Two bodies $A$ and $B$ of masses $m$ and $2m$ respectively are placed on a smooth floor. They are connected by a spring. A third body $C$ of mass $m$ moves with velocity $V_0$ along the line joining $A$ and $B$ and collides elastically with $A$ as shown in fig. At a certain instant of time $t_0$ after collision, it is found that instantaneous velocities of $A$ and $B$ are the same. Further at this instant the compression of the spring is found to be $x_0$. Determine the spring constant

$A$ ball of mass $m$ is attached to the lower end of light vertical spring of force constant $k$. The upper end of the spring is fixed. The ball is released from rest with the spring at its normal (unstretched) length, comes to rest again after descending through a distance $x.$

In the diagram shown, no friction at any contact surface. Initially, the spring has no deformation. What will be the maximum deformation in the spring? Consider all the strings to be sufficiency large. Consider the spring constant to be $K$.

A spring with spring constant k when stretched through $1\, cm$, the potential energy is $U$. If it is stretched by $4 \,cm.$ The potential energy will be

Two blocks each of mass $m$  are connected to a spring of spring constant $k.$  If both are given velocity $v$  in opposite directions, then the maximum elongation of the spring is