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Restoring force, in a physics context, is a variable force that gives rise to an equilibrium in a physical system. If the system is perturbed away from the equilibrium, the restoring force will tend to bring the system back toward equilibrium. The restoring force is a function only of position of the mass or particle. It is always directed back toward the equilibrium position of the system.
The restoring force is often referred to in simple harmonic motion.
An example is the action of a spring. An idealized spring exerts a force that is proportional to the amount of deformation of the spring from its equilibrium length, exerted in a direction to oppose the deformation. Pulling the spring to a greater length causes it to exert a force that brings the spring back toward its equilibrium length. The amount of force can be determined by multiplying the spring constant of the spring by the amount of stretch.
Another example is of a pendulum. When the pendulum is not swinging all the forces acting on the pendulum are in equilibrium. The force due to gravity and the mass of the object at the end of the pendulum is equal to the tension in the string holding that object up. When a pendulum is put in motion the place of equilibrium is at the bottom of the swing, the place where the pendulum rests. When the pendulum is at the top of its swing the force bringing the pendulum back down to this midpoint is gravity. As a result gravity can be seen as the restoring force in this case.
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