Initially,a spring is at its natural length. $A$ block of mass $2 \, kg$ is attached to the lower end,and a block of mass $0.25 \, kg$ is at the top. If the system is released from the position where the spring is at its natural length,find the maximum force exerted by the system on the floor? (in $N$,take $g = 10 \, m/s^2$)

The system shown in the figure is in equilibrium and at rest. The spring and string are massless. Now, the string is cut. The acceleration of mass $2m$ and $m$ just after the string is cut will be:

$A$ spring of force constant $k$ is cut into lengths of ratio $1:2:3$. They are connected in series and the new force constant is $k'$. Then they are connected in parallel and the force constant is $k''$. Then $k':k''$ is

$A$ block of mass $2 \,kg$ is connected to an ideal spring and is placed on a smooth horizontal surface. The spring is pulled to move the block and at an instant, the speed of end $A$ of the spring and speed of the block were measured to be $6 \,m/s$ and $3 \,m/s$, respectively. At this moment, the potential energy stored in the spring is increasing at a rate of $15 \,J/s$. Find the acceleration of the block at this instant. (in $\,m/s^2$)

$A$ spring with $10$ coils has spring constant $k$. It is exactly cut into two halves,then each of these new springs will have a spring constant

Two springs having spring constants $k_1$ and $k_2$ are connected in series,their resultant spring constant is $2 \text{ unit}$. If they are connected in parallel,their resultant spring constant is $9 \text{ unit}$. Find the values of $k_1$ and $k_2$.