Which equation represents the spring constant?

The spring constant is a measure of a spring's stiffness and is represented in Hooke's Law, which describes how the force exerted by a spring is proportional to its displacement from the equilibrium position. The fundamental equation is expressed as F = -kx, where F is the force exerted by the spring, k is the spring constant, and x is the displacement from the equilibrium position. The negative sign indicates that the force exerted by the spring is in the opposite direction to the displacement, meaning the spring resists the stretching or compression.

Choosing the correct equation involves recognizing that the spring constant can be articulated through both forms: the basic formulation F = kx describes the direct relationship where the force is positive when the spring is compressed, and F = -kx highlights the reactionary force given by the spring. Thus, both of these expressions effectively convey the relationship defined by Hooke’s Law.

In this context, while F = k/x and other forms may appear, they do not accurately represent the relationship inherent in the behavior of spring forces as described by Hooke's Law. Therefore, recognizing that both F = kx and F = -kx collaboratively express the relationship governed by the spring constant provides a complete picture of how springs respond to forces