$A$ spring of force constant $k$ is cut into two equal halves. The force constant of each half is

An ideal spring with spring-constant $K$ is hung from the ceiling and a block of mass $M$ is attached to its lower end. The mass is released with the spring initially unstretched. Then the maximum extension in 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:

When a weight is applied to a spring,it stretches by an amount $x$. What is the energy stored in it? ($T$ is the tension force developed in the spring and $k$ is the spring constant.)

$A$ spring of force constant $k$ is cut into two pieces such that one piece is three times the length of the other. The longer piece will have a force constant of

One-fourth length of a spring of force constant $K$ is cut away. The force constant of the remaining spring will be