Question

Why is the restoring force in Hooke's law a negative value?

Answer 1

The negative sign is used because F is the restoring force of the spring, which is in the opposite direction from the applied force of the hanging mass.The restoring force is therefore in the opposite direction from the displacement of the spring.
@department of Physics Astronomy

Answer 2

The spring force is Hooke's law is called restoring force because thee force exerted by the spring is always in the opposite direction the displacement. This is why there is a negative sign in the Hooke's law with the restoring force.