According to Hooke's law, what is the relationship between the force applied to a spring and its extension?

Hooke's law states that the extension of a spring is directly proportional to the force applied to it, provided the limit of proportionality is not exceeded. This means that if you double the force applied to the spring, the extension also doubles. The relationship can be described mathematically as F = kx, where F is the force applied, k is the spring constant, and x is the extension of the spring. This linear relationship emphasizes that as the force increases, the extension increases in a predictable, proportional manner, highlighting the simple and direct relationship dictated by Hooke's law.