Hooke's Law for springs describes the relationship between force and displacement as which of the following?

• A. F = ma (the force equals mass times acceleration)
• B. F = mg (weight equals mass times gravity)
• C. F = kx (the force is proportional to displacement)
• D. F = -kx (the restoring force opposite displacement)

Answer: (C)

Hooke's Law shows that a spring’s force grows linearly with how far you pull or compress it. The essential idea is proportionality: the force’s magnitude is the spring constant k times the displacement x from equilibrium. The constant k tells you how stiff the spring is—the larger k, the greater the force for the same displacement. The full expression F = -kx adds the direction, indicating the force acts opposite to the displacement (a restoring force). So, describing the relationship between force and displacement, the magnitude is proportional, F = kx. The other forms don’t capture this specific link to displacement: F = ma is about motion, F = mg is weight, and F = -kx includes direction but is the same idea with a sign.