How is the spring coefficient k_s calculated? What exactly is stiffness for a spring?
The k_s should be a given coefficient when you have a spring. It's like an attribute to a spring. Every spring might differ in this stiffness.
Hooke's law can also be expressed in terms of strain and stress! Stress is the force per unit area that is needed to create elastic deformation of the object. The fractional change in quantity that results when stress is applied is called strain. In other words, strain is the reflative deformation produced by stress. The SI unit of stress is pascal (Pa) while strain is dimensionless.