Statement: “the force needed to extend or compress a spring by some distance is proportional to that distance.” and this can be written as:
F = -kx …………………………(1)
Where F is the force, x is the length of extension/compression and k is a constant of proportionality known as the spring constant which is usually given in N/m. The negative sign is to signify that the restoring force due to the spring is in the opposite direction to the force which caused the displacement. Pulling down on a spring will cause an extension of the spring downward, which will, in turn, result in an upward force due to the spring.
|Figure 1. Stress and strain to understand the Hook’s Law|