Hooke's law:
Hooke’s law, law of elasticity discovered by the English scientist Robert Hooke in 1660, which states that, for relatively small deformations of an object, the displacement or size of the deformation is directly proportional to the deforming force or load. Under these conditions the object returns to its original shape and size upon removal of the load.
Hooke's law is return as:
\[F = - k\Delta x \]
where F is the force applied to the spring (either in the form of strain or stress);\[\Delta x \] is the displacement of the spring, with a negative value demonstrating that the displacement of the spring once it is stretched; and k is the spring constant.
When calculating \[\Delta x \] , it is important to remember that the spring itself will also have some nominal length L0, subscript. The total L of a spring under extension is equal to the nominal length plus the extension,\[\Delta x \] =L0 + x . For a spring under compression, it would be \[\Delta x \]=L0-x
