The potential energy of a long spring when it is stretched by $3 \ cm$ is $U$. If the spring is stretched by $9 \ cm$,the potential energy stored in it will be: (in $U$)

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 $k_2$.

$A$ 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:

$A$ 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

Two blocks each of mass $m$ are connected to a spring of spring constant $k.$ If both are given velocity $v$ in opposite directions,then the maximum elongation of the spring is

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