$A$ block is attached to a spring as shown and very gradually lowered so that finally the spring expands by $d$. If the same block is attached to the spring and released suddenly,then the maximum expansion in the spring will be:

$A$ block of $3 \; kg$ is initially in equilibrium and is hanging by two identical springs $A$ and $B$ as shown in the figure. If spring $A$ is cut from the lower point at $t = 0$,find the acceleration of the block in $m/s^2$ at $t = 0$.

$A$ 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

The force constant of a spring is $K$. If half of the spring is cut off,what will be the force constant of the remaining spring?

$A$ block of mass $M$ is attached to the lower end of a vertical spring. The spring is hung from a ceiling and has a force constant $k$. The mass is released from rest with the spring initially unstretched. The maximum extension produced in the length of the spring will be

Find the acceleration of the $3 \text{ kg}$ mass when the acceleration of the $2 \text{ kg}$ mass is $2 \text{ ms}^{-2}$ as shown in the figure. (in $\text{ ms}^{-2}$)