Hooke's Law

Hooke’s law says that, for a spring or spring-like object, the force it exerts grows in direct proportion to how far it is stretched or compressed from its natural length. The minus sign shows that the force acts in the opposite direction to the displacement, so the spring always tries to return to equilibrium. This works well only while the material stays within its elastic limit, where the spring’s behavior remains approximately linear.

Use this formula when dealing with springs, elastic bands modeled as springs, or any situation where you need the restoring force from a small extension or compression. It is common in mechanics problems involving equilibrium, oscillations, and stored elastic energy.

• Forgetting the negative sign and treating the force as acting in the same direction as the displacement
• Using the formula beyond the elastic limit, where force is no longer proportional to extension
• Mixing up the spring constant units, which should be newtons per meter (N/m)