What is the restoring force on a spring that is stretched by x from its equilibrium position?

What is the restoring force on a spring that is stretched by x from its equilibrium position?

• A. F = k x
• B. F = - k x
• C. F = m g
• D. F = - m g

Answer: (B)

A spring resists displacement with a restoring force that pulls back toward equilibrium. Hooke’s law states the restoring force has magnitude kx and acts opposite to the direction of the stretch. So when the spring is stretched by x, the force on the attached mass points toward the equilibrium position with magnitude kx, written as F = -k x. The negative sign is what keeps it directed back toward balance. Gravity (mg) is a separate force and not the spring’s restoring force, and F = kx would point in the same direction as the stretch, not toward the equilibrium.

A spring resists displacement with a restoring force that pulls back toward equilibrium. Hooke’s law states the restoring force has magnitude kx and acts opposite to the direction of the stretch. So when the spring is stretched by x, the force on the attached mass points toward the equilibrium position with magnitude kx, written as F = -k x. The negative sign is what keeps it directed back toward balance. Gravity (mg) is a separate force and not the spring’s restoring force, and F = kx would point in the same direction as the stretch, not toward the equilibrium.