What is the type of force that acts on a spring? Explain work energy theorem with respect to a spring.

Explanation

The type of force that acts on a spring is a conservative force and as well as a variable force. The force law also called as Hooke's law with respect to the force on the spring `f_(s)=-kx`
where k - is known as the spring constant in `Nm^(-1)` and x - is elongation. For a compression the displacement will be '-x' so that `F_(s)=+kx`.
For extension `W_(s)=underset(0)overset(x_(m))intF_(s)dx=-underset(0)overset(x_(m))intkxdx=-(kx_(m)^(2))/(2)`
The work done by the spring force for displacement `x_(i)` to `x_(f)` is given by
`W_(s)=-underset(x_(i))overset(x_(f))intkxdx=-(k)/(2)(x_(i)-x_(f))`
It is clear that if the spring returns to initial state W = 0. Since there is no loss in the energy, and the force is retrieved, the force is conservative.
Using `(1)/(2)mv_(m)^(2)=(1)/(2)kx_(m)^(2)`
We get `v_(m)=sqrt((k)/(m)).x_(m)`