In a mass-spring system, the restoring force direction relative to displacement is?

• A. Opposite to the displacement
• B. In the same direction as the velocity
• C. Perpendicular to the displacement
• D. Unrelated to displacement

Answer: (A)

The restoring force in a mass-spring system always points opposite to how far the mass is from equilibrium. Hooke’s law, F = -k x, says the force is proportional to the displacement x and directed opposite to it, pulling the mass back toward equilibrium. So if you stretch the spring to the right, the force pulls left, and if you compress it to the left, the force pulls right. This opposite-direction push/pull is what creates the oscillatory motion, as the force changes direction with the displacement. The other possibilities don’t fit: a force along the velocity would augment motion rather than restore it, a force perpendicular to displacement wouldn’t oppose the displacement, and a force unrelated to displacement wouldn’t drive the system back toward equilibrium.