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Hooke’s Law? What Does That Mean For Your Springs?

Hooke’s Law, discovered in 1660, describes the elasticity, torsion and force of springs, making it extremely important when it comes to the design and use of springs for compressors.

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Springs are created as a result of human engineering and creativity – And the best way to understand how springs work is to gain an understanding of their mechanics. These mechanics have been explained by Hooke’s Law, a principle that describes the elasticity, torsion, and force of springs.

On the other hand, compression springs, torsion springs, coil springs, and even extension spring design store mechanical energy. As such, they serve different and specific functions. The functions provided by these springs enable the creation of other objects.

What’s more, there are various types of springs; hence, it becomes needful to resort to the expertise of an experienced spring manufacturer to determine the spring and type of material that is suitable in your application.

Application of Springs

Springs are elastic objects that store mechanical energy and they have an extensive application. They can be used in the following devices:

  • Watches
  • Hand sheers
  • Compressors
  • Wind-up toys
  • Pendulum clocks
  • Digital micromirror devices

What is Hooke’s Law?

Hooke’s law is named after Robert Hooke, a 17th century British Physicist who investigated the relationship between the forces applied to a spring and its elasticity. His aim was to discover how springs and elastic materials stretch, and that being the case, his law is a first-order linear approximation to the real response of springs to applied forces.

Hooke’s law states that the force needed to extend or compress a spring by some distance is proportional to the distance moved by the spring.

What this simply means is the more you stretch a spring, the harder it becomes to stretch it – and this is a linear relationship. This law also outlines that spring will always stretch the same length when it is pushed or pulled.

A range of materials obey this law, however, when the elasticity of the spring is exhausted by the load, then this law is not obeyed.

That aside, Hooke’s law was first stated in 1676 as a Latin anagram. In 1678, he published a solution of his anagram and it was “ut tensio, sic vis,” meaning “as the extension, so the force”

Mathematical Representation of Hooke’s Law

Hooke’s law mathematically represents a linear spring that is pushed or pulled in one direction as:


or equivalently,


  • F represents the force on the spring and it is measured in newtons.
  • k is a constant that indicates the spring’s stiffness
  • X is the distance the spring is pushed or pulled and it is measured in meters. Its negative value represents a displacement when the spring is pushed or pulled.

The above can be applied to a simple helical spring which has an end attached to a fixed object, while its free end is pulled by a force whose magnitude is Fs.

If this spring has reached a state of equilibrium where its length is no longer changing, X, can represent the amount by which the free end of the spring was displaced.

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What is Elasticity?

A property of spring to return to its original position after being stretched is called elasticity. Hooke’s law is one of the earliest explanations of elasticity.

The spring constant also relates to elasticity, and this spring constant is a number that represents the amount of force required to stretch a material. The larger the spring constant of a material, then the stiffer the spring.

There are, however, materials that are not elastic, hence, they may tend to snap even before they are bent or stretched. The latter can be attributed to their brittle nature.

What is the Restoring Force?

Restoring force can be attributed as to what causes a stretched spring to return to its original position. Based on Hooke’s law, the restoring force is proportional to the amount of stretch experienced.

In other words, as you stretch a spring, you will also need to compete with a restoring force. This restoring force is trying to restore the object to its original position.

Limitation of Hooke’s Law in Springs

A spring material cannot be stretched beyond its maximum size without a deformity occurring or change in its state. Similarly, a material cannot be compressed beyond a certain minimum size.

That being the case, Hooke’s law is only applicable when the limit amount of force is exerted on the material.

On the same note, some materials may deviate from Hooke’s law even before their elasticity limit is reached. Despite this limitation, Hooke’s law is still an accurate approximation when it comes to most solid bodies. In this case, the forces and deformation must be small.

Hooke’s law is also the fundamental principle behind the spring scale, balance wheel of the mechanical clock, and the manometer.

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Comparison of Hooke’s Law with the Law of Thermodynamics

Hooke’s law can be compared with the law of Thermodynamics which states that energy can neither be created nor destroyed, but moves from one form to the other.

In this case, a stretched or compressed spring conserves most of the energy applied to it. However, energy may still be lost to natural friction.

Over and above that, Hooke’s law has a wave-like periodic function. In this case, a spring that has been released from a deformed position will move to its original position with proportional force repeatedly in a periodic function.


Springs are of various types and they serve a range of functions, which has enabled the creation of several objects. Also, the mechanics of these springs give a better understanding of how they operate and the potential uses they can be put to.

Hooke’s law, on the other hand, has demonstrated the forces, elasticity, and torsion of springs. Despite this, there are certain conditions where the law will not hold, especially if the stretch or compress limit of the spring has been exhausted.

Asides from Hooke’s law, the modern theory of elasticity gives a generalized version of Hooke’s law; it states that the strain/deformation of an elastic object is proportional to its applied stress.

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