$A$ spring with force constant $k$ is cut into two pieces. The length of one piece is twice the length of the other. What is the force constant of the larger piece?

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, $k$)

Two masses of $10\, kg$ and $20\, kg$ respectively are connected by a massless spring as shown in the figure. $A$ force of $200\, N$ acts on the $20\, kg$ mass. At the instant when the $10\, kg$ mass has an acceleration of $12\, m\, s^{-2}$,the acceleration of the $20\, kg$ mass is ...... $m\, s^{-2}$.

$A$ simple 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:

Infinite springs with force constants $k$,$2k$,$4k$,$8k$,... respectively are connected in series. The effective force constant of the system will be:

In the figure,blocks $A$ (mass $2m$) and $B$ (mass $m$) are connected with a string and the system is suspended vertically with the help of a spring. The spring has negligible mass. Find the magnitude of the acceleration of masses $2m$ and $m$ just after the instant when the string is cut.