Which of the following expressions represents Hooke's law, where Fs is a spring force?

Hooke's law is a fundamental principle of elasticity that describes how a spring behaves when it is compressed or stretched. The expression that represents Hooke's law is ( F_s = -kx ).

In this equation, ( F_s ) is the spring force, ( k ) is the spring constant (which measures the stiffness of the spring), and ( x ) is the displacement of the spring from its equilibrium position. The negative sign indicates that the spring force acts in the opposite direction to the displacement. This means that if you stretch the spring (making ( x ) positive), the spring exerts a force back toward its equilibrium position, which is consistent with the idea of restoring force. Conversely, if the spring is compressed (making ( x ) negative), the force also acts to restore it to equilibrium.

The other expressions do not accurately reflect the relationship described by Hooke's law. The expression ( F_s = kx ) lacks the crucial negative sign, which means it does not indicate the direction of the spring force. Meanwhile, ( F_s = kx^2 ) implies a nonlinear relationship, which is not the case for springs behaving elastically within their limits. Lastly, ( F_s =