When a force (Fa) is applied to the spring, it will stretch by a certain amount.
Its new position will be X2
The amount of stretch is given by the change from position X1 to position X2.
This change in position is ∆X.
∆X.= X2 - X1
The amount of stretch (∆X) is proportional to the applied force Fa.
Graphically, this relationship can be shown as:
Hooke's Law tells us that the force required to stretch a spring is given by
Fnet = k∆X
Therefore, the amount of "restoring force" required to bring the spring back to its equilibrium position is
Fnet = -k∆X