Springs. Properties and Hooke’s law

09/05/2026

The online spring simulations on this page teach us in a practical way how these devices work, what are the forces acting on themthat act, how they store energy, and what Hooke’s law tells us, what is the elastic constant and what are the main properties of springs.

This Thematic Unit is part of our Physics collection

Damping

Energy dissipation process in an oscillatory system that gradually reduces the amplitude of motion.

Deformation

Change in the length or shape of an elastic body (stretching or compression) relative to its equilibrium position.

Elastic Limit

Maximum deformation a material can withstand without undergoing permanent changes in its shape.

Elastic Potential Energy

Energy stored in an elastic body when deformed, which is released when it returns to its original shape.

Hooke’s Law

Physical principle stating that the force exerted by a spring is proportional to its deformation, measured in joules (J) regarding work performed.

Oscillation

Repetitive back-and-forth motion of a body passing through an equilibrium position.

Restoring Force

Force that tends to return a system to its equilibrium position and is proportional to the displacement.

Spring Constant

Value indicating a spring’s stiffness, representing the force required to produce a unit of deformation (N/m).

What is a spring

A spring is a flexible and elastic mechanical device used to store elastic potential energy and apply force when deformed. It consists of a strip, wire or rod of elastic material, such as steel or metal, that has a coiled, spiral or zigzag shape. When a spring is compressed or stretched, it stores potential energy in the form of elastic deformation, and when released, that energy is converted into kinetic energy.

Springs can have different shapes and configurations depending on their specific use. Some common examples include compression springs, extension springs and torsion springs.

Properties of springs. Hooke’s law and elastic constant

The properties of springs are governed by Hooke’s Law, which states the linear relationship between the force applied on a spring and the resulting deformation. Hooke’s Law is stated as F = -kx, where F represents the applied force, k is the spring constant (also known as the elastic constant) and x is the deformation experienced by the spring. The equation indicates that the force is proportional to the deformation and acts in the opposite direction to it.

Strictly speaking, Hooke’s Law is a valid approximation as long as the deformation is small and the spring material maintains its linear elastic behavior. However, at larger deformations, other factors such as plasticity and fatigue can affect the spring response.

Applications of springs

Springs have a huge variety of applications: automotive suspensions, watches, mattresses, automatic doors and many more.

Damping

Energy dissipation process in an oscillatory system that gradually reduces the amplitude of motion.

Deformation

Change in the length or shape of an elastic body (stretching or compression) relative to its equilibrium position.

Elastic Limit

Maximum deformation a material can withstand without undergoing permanent changes in its shape.

Elastic Potential Energy

Energy stored in an elastic body when deformed, which is released when it returns to its original shape.

Hooke’s Law

Physical principle stating that the force exerted by a spring is proportional to its deformation, measured in joules (J) regarding work performed.

Oscillation

Repetitive back-and-forth motion of a body passing through an equilibrium position.

Restoring Force

Force that tends to return a system to its equilibrium position and is proportional to the displacement.

Spring Constant

Value indicating a spring’s stiffness, representing the force required to produce a unit of deformation (N/m).

Explore the exciting STEM world with our free, online, simulations and accompanying companion courses! With them you’ll be able to experience and learn hands-on. Take this opportunity to immerse yourself in virtual experiences while advancing your education – awaken your scientific curiosity and discover all that the STEM world has to offer!

Spring simulations

Force of a spring

One of the main properties of springs is the one that refers to their force.

Work on a spring

Energy in a spring

Another of the main properties of springs is the one that refers to their energy.

Hooke’s Law and elastic constant

Hooke’s law governs the properties of springs. Stretch and compress springs to explore the relationships between force, spring constant, displacement and potential energy! Investigate what happens when two springs are connected in series and parallel.

Masses and springs I

Hang masses from springs and discover how they stretch and oscillate. Compare two spring mass systems and experiment with the spring constant. Transport the lab to different planets, slow down time, and observe velocity and acceleration throughout the oscillation.

Masses and springs II

Hang masses on springs and adjust the spring constant and damping. Transport the lab to different planets, or slow down time. Observe the forces and energy in the system in real time and measure the period using the stopwatch.

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“If I have seen further, it is by standing on the shoulders of giants”

Isaac Newton

Leonhard Euler

1707

–

1783

Euler developed much of modern mathematical notation and made key contributions to analysis, topology, mechanics, and graph theory

“Nothing takes place in the universe without mathematics expressing it”

Daniel Bernoulli

1700

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1782

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“Give me a place to stand, and I will move the world”

Augustin-Louis Cauchy

1789

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1857

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“Rigor in mathematics is the key to understanding physical phenomena”

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Test your knowledge

What is a spring, and what role does it play in terms of energy and force within a mechanical system?

A spring is a flexible, elastic mechanical device designed to store elastic potential energy when it is deformed and release it later as kinetic energy, and it is usually made from a strip or wire of an elastic material such as steel, shaped into a spiral, zigzag or other geometry depending on its application. When compressed or stretched, the spring accumulates energy due to the deformation of its internal structure, and when released it returns to its original shape by applying a force that depends on its elastic constant, which makes it essential in systems that need to absorb impacts, generate motion, maintain tension or allow controlled oscillations.

How does Hooke’s law describe the behavior of a spring, and under what conditions is this relationship valid?

Hooke’s law states that the force exerted by a spring is proportional to the deformation it undergoes and acts in the opposite direction, meaning that the more a spring is stretched or compressed, the greater the force it produces to return to its equilibrium position. This linear relationship is valid as long as the deformation is small and the material behaves elastically, but when the spring is subjected to large deformations effects such as plasticity, fatigue or loss of linearity can appear, so Hooke’s law works as a very useful approximation in most practical applications, but with limits defined by the material’s properties.

Why are there so many different types of springs? Sometimes it feels like they all do the same thing.

Even though they all store elastic energy, each type is designed for a specific function: compression springs handle loads that push them inward, extension springs work when they are stretched, and torsion springs respond to twisting, so it’s not that they exist “just because,” but because each application needs a different way of deforming and releasing energy.

Why does a spring give the energy back when I let it go? It’s almost like it “remembers” its shape.

What happens is that the material of the spring tries to return to its original state because its internal structure gets deformed when you stretch or compress it, and that deformation stores energy that is released when you let go, so it’s not real memory but simply the natural tendency of the material to recover its shape to minimize internal energy.

Why are springs so good for making things oscillate? I always see them in vibration experiments.

Springs allow oscillations because when they are stretched or compressed they generate a force that pushes the system back toward its equilibrium position, and if a mass is attached to the spring, that force makes the system move back and forth repeatedly, so a spring and a mass together form a perfect setup for studying vibrations, energy and periodic motion.