The potential energy of a weight less spring compressed by a distance $ a $ is proportional to

$A$ 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 the normal reaction $N$ between the block and the spring on the block is

Find the maximum tension in the spring if initially spring at its natural length when block is released from rest.

The figure shows a mass $m$ on a frictionless surface. It is connected to rigid wall by the mean of a massless spring of its constant $k$. Initially, the spring is at its natural position. If a force of constant magnitude starts acting on the block towards right, then the speed of the block when the deformation in spring is $x,$ will be

If a long spring is stretched by $0.02\, m$, its potential energy is $U$. If the spring is stretched by $0.1\, m$ then its potential energy will be

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: $Image$