A compressed or stretched spring exerts a restoring force on a mass attached to it. The restoring force always acts opposite to the deformation of the spring to bring the spring back to its original length. Therefore, when the spring is stretched, the restoring force compresses it and conversely when it is compressed, the restoring force stretches it. As a result, the restoring force will tend to return the mass to its equilibrium position (when the spring is neither compressed nor stretched).
For small deformations, when the spring has not reached its elastic limit, the restoring force is proportional to the deformation of the spring and is given by the Hooke’s law:
where i is a unit vector and x the deformation of the spring measured with respect to its natural length (when the spring is neither compressed nor stretched).
K is the stiffness of the spring and its value depends on the properties of the material and the geometry of the spring. Its units in the International System (SI) are N/m.
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The following figure shows a mass attached to a spring and the forces acting on it.
You will find on these pages many problems describing how to work with the restoring force of a spring in different situations.
Here you can find Newton’s laws problems.