To find a general equilibrium point for a spring based on the hook law, it is possible to start from the following premise:
Hook's law is given by:
[tex]F = k\Delta X[/tex]
Where,
k= Spring Constant
[tex]\Delta X =[/tex] Change in Length
F = Force
When there is a Mass we have two force acting at the System:
W= mg
Where W is the force product of the weigth. Then the force net can be defined as,
[tex]F_{net} = F+W[/tex]
But we have a system in equilibrium, so
[tex]0 = K\Delta X -mg[/tex]
We find the equilibrium for any location when
[tex]\Delta X = \frac{mg}{k}[/tex]
