where is the displacement of the spring from its natural length. We call the spring constant, or stiffness of the spring. In terms of our previous notation, we have
Note that the force on the spring in Fig.B.1 is gravitational force. Equal and opposite to the force of gravity is the spring force exerted upward by the spring on the mass (which is not moving). We know that the spring force is equal and opposite to the gravitational force because the mass would otherwise be accelerated by the net force.B.4 Therefore, like gravity, a displaced spring can be regarded as a definition of an applied force. That is, whenever you have to think of an applied force, you can always consider it as being delivered by the end of some ideal spring attached to some external physical system.
Note, by the way, that normal interaction forces when objects touch arise from the Coulomb force (electrostatic force, or repulsion of like charges) between electron orbitals. This electrostatic force obeys an ``inverse square law'' like gravity, and therefore also behaves like an ideal spring for small displacements.B.5
The specific value of depends on the physical units adopted as well as the ``stiffness'' of the spring. What is most important in this definition of force is that a doubling of spring displacement doubles the force. That is, the spring force is a linear function of spring displacement (compression or stretching).
Applying Newton's Laws of Motion