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 $2m$?

$A$ spring has length $L$ and force constant $K$. It is cut into two springs of length $L_1$ and $L_2$ such that $L_1 = N L_2$ ($N$ is an integer). The force constant of the spring of length $L_1$ is:

Fill in the blank: The force constant of a spring is $0.5 \, Nm^{-1}$. The force necessary to increase the length of the spring by $10 \, cm$ will be .......... (in $, N$)

To the free end of a spring hanging from a rigid support, a block of mass $m$ is hung and slowly allowed to come to its equilibrium position. Then the stretching in the spring is $d$. If the same block is attached to the same spring and allowed to fall suddenly, the amount of maximum stretching is: (force constant, $k$)

Give an example of a variable force. Write the formula for Hooke's law.

The tension in the spring is