A block attached with a spring is kept on a smooth horizontal surface. Now the free end of the spring is pulled with a constant velocity $u$ horizontally. Then the maximum energy stored in the spring and block system during subsequent motion is

Blocks $A$ and $B$ of mass $m$ each are connected with spring of constant $k$. Both blocks lie on frictionless ground and are imparted horizontal velocity $v$ as shown when spring is unstretched. Find the maximum stretch of spring.

Find the maximum compression in the spring, if the lower block is shifted to rightwards with acceleration $a$. All the surfaces are smooth.

The block of mass $m$ initially at $x = 0$ is acted upon by a horizontal force $F=a - b{x}^2$(where $a>\mu mg$) as shown in the figure. The co-efficient of friction between the surfaces of contact is $\mu$. The net work done on the block is zero, if the block travels a distance of

The components of a force acting on a particle are varying according to the graphs shown. When the particle moves from $(0,5,12)$ to $(4,20,0)$ then the work done by this force is

In the figure shown, initially, spring is in an unstretched state and blocks are at rest. Now $100 \mathrm{N}$ force is applied on block $A$ and $B$ as shown in the figure. After some time velocity of $A$ becomes $2 \mathrm{m} {\mathrm{s}}^{-1}$ and that of $B$ $4 \mathrm{m} {\mathrm{s}}^{-1}$ and block $A$ displaced by amount $10 \mathrm{cm}$ and spring is stretched by amount $30 \mathrm{cm}$. Then work done by spring force on $A$ will be: