Which statement best describes Hooke's Law for a spring?

• A. The force exerted by a spring is in the same direction as displacement and proportional to displacement.
• B. The force exerted by a spring is opposite to displacement and proportional to displacement.
• C. The force exerted by a spring is independent of displacement.
• D. The force exerted by a spring is proportional to velocity.

Answer: (B)

When a spring is displaced from its rest length, the restoring force it exerts acts to bring it back toward equilibrium, and this force grows in proportion to how far you’ve stretched or compressed it. The direction is opposite to the displacement, which is what makes the spring push back toward the starting position. This relationship is written as F = -k x, where k is the spring constant and x is the displacement from equilibrium; the negative sign ensures the force is restorative.

If the force were in the same direction as the displacement, it would push the spring farther away instead of restoring it, which isn’t how a real spring behaves. If the force didn’t depend on displacement, there would be no spring-like behavior at all. If the force depended on velocity, that would describe damping, not Hooke’s law. So the statement that best describes Hooke’s Law is that the force is opposite to displacement and proportional to it.