Restoring force is defined as the force responsible for bringing a body back to its original shape, size, and position. Shrinking and expanding of spring involves restoring force. It is a kind of conservative force. The tendency of a pendulum to be in the middle is an example of restoring force. Restoring force is a concept related to simple harmonic motion. Restoring force directly varies with the displacement made from the original position or rest position.

Restoring Force of Spring

When the end of a spring is fixed on a frictionless surface and is left untouched, that position is called the rest position or at equilibrium state. At this point, no external force and restoring force are acting on it. When the other end of that spring is stretched or compressed with the help of a force acting on it, the spring also exerts some force in the opposite direction on that mass. As soon as the external force is removed, the spring exerts its restoring force, which is proportional to the displaced length of the spring and comes back to its equilibrium state by shrinking or relaxing. The force required by the spring to come back to its original position is the restoring force. This has been explained below: 

• No displacement, external force, or restoring force exists when the spring is at rest.
• When compressing the spring, the displacement and external force are in the left direction, and the restoring force is acting in the right direction.
• While stretching the spring, the displacement and external force is in the right direction, and the restoring force is acting in the left direction.

Restoring Force in Pendulum

A pendulum is a system in which a mass is suspended with the help of a cord and makes back and forth movements. When the pendulum does not move, it is said that it is at rest and is in equilibrium. At this point, two working forces on the pendulum, gravitational force and tension,  are in equilibrium.

Simple Harmonic Motion (SHM) Formula

As per Hooke’s Law, the simple harmonic motion formula for restoring force F of a spring when it is extended or compressed by length x is given as:

F=-kx  or F=-k(b-a), where k is the constant of the given spring, and a and b are the initial and final lengths of the spring, respectively.

The constant k in the above shm equations is also called the force constant or spring constant. Depending upon the stiffness of springs, different springs have different values of the constant k. The value of k is always positive. 

The negative sign in the SHM equations means that the force and the displacement are in opposite directions. When the spring is stretched, the displacement is outwards while the restoring force acts inwards, tending to restore the spring to its equilibrium state. Similarly, when the spring is compressed, the displacement happens inwards, and the restoring force acts outwards, tending to bring back the spring to its original state of equilibrium.

Properties of Elastic Restoring Force

The restoring force of a spring, when it is connected to two objects on each side, possesses the following properties:

• The spring exerts equal and opposite force on both objects.
• When the spring is at equilibrium, it exerts no force on any of the objects.
• When the spring is stretched beyond its original length, the restoring force is exerted on both the objects and tends to bring them together.
• When the spring is compressed beyond its original length, the restoring force is exerted on both the objects and tends to push them away towards the end.
• The magnitude of the restoring force is directly proportional to the displaced length of the spring.

Conclusion

In this article, we get to know that the restoring force always acts in the opposite direction of the displacement in the body. The restoring force is the greatest when maximum displacement happens, and ultimately the acceleration is also maximum. When a body is not moving and is in its equilibrium position, the restoring force, as well as acceleration, is zero.