Two blocks are connected by a spring. The combination is suspended,at rest,from a string attached to the ceiling,as shown in the figure. The string breaks suddenly. Immediately after the string breaks,what is the initial downward acceleration of the upper block of mass $2m$?

$A$ 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 $t = 0$.

Two springs $A$ and $B$ are fixed at the top and are stretched by $8 \,cm$ and $16 \,cm$ respectively, when loads of $20 \,N$ and $10 \,N$ are suspended at the lower ends. The ratio of the spring constants of the springs $A$ and $B$ is (in $: 1$)

$A$ 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

$A$ body of mass $m$ is tied to one end of a spring and whirled round in a horizontal plane with a constant angular velocity. The elongation in the spring is $1 \, cm$. If the angular velocity is doubled,the elongation in the spring is $5 \, cm$. The original length of the spring is ............ $cm$.

$A$ 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 $\,m/s^2$)