Question

Why the force constant of spring is always positive?

Answer 1

Spring constants are always positive. The displacement, x, from equilibrium is actually a vector quantity, which means it is the quantity that carries the sign (indicating direction). Which direction is positive or negative (stretching or compressing) is, I believe, a matter of choice, as long as you can remain consistent with the direction throughout the problem (usually, though, I consider compression to be a negative displacement, and extension to be positive). The real center of Hooke's law, though, is that the force is always directed opposite the displacement