According to Hooke's Law as stated, what is the restoring force F_s when displacement is x?

• A. F_s = -kx
• B. F_s = k/x
• C. F_s = kx
• D. F_s = mg

Answer: (C)

The restoring force from a spring is directed opposite to how the spring is displaced and grows in magnitude with that displacement. Hooke's Law is F_s = -k x, where k is the spring constant and x is the displacement from equilibrium. The negative sign means the force points back toward equilibrium: if you pull the spring to the right (positive x), the force pulls it left; if you push it to the left (negative x), the force pulls it right. The magnitude is |F_s| = k|x|. The other forms don’t fit this behavior: F_s = k/x isn’t proportional to x, F_s = kx points in the same direction as the displacement, and F_s = mg is a gravitational force, not the spring’s restoring force.