# Mathematics behind Hooke's law

• eseefreak
In summary, The conversation discusses the confusion surrounding the three different formulas for Hooke's law and the work done by a spring. The speaker is trying to understand the mathematical reasoning behind the three formulas and why they are specific to certain problems. They also mention that the first expression is a general case that can be derived from the other formulas.

#### eseefreak

I'm trying to understand the math behind Hooke's law and work done by a spring. I'm really looking for clarity. I am trying to understand why after integrating the equation I get three different results. I understand that each formula is specific to a problem but why does this work mathematically? I attached an image of the three formulas together.

Thank you. Much appreciated

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I think they are a little confusing (or confused).
What they call "specific" is actually the general case, the work done by the elastic force between any two arbitrary positions. The first expression is just what you get from the general one, for the particular case of initial position xf=0 and xi=x_max.

## 1. What is Hooke's law?

Hooke's law is a principle in physics that describes the relationship between the force applied to an object and the resulting displacement of that object. It states that the force applied to an elastic object is directly proportional to the amount of stretch or compression of the object.

## 2. Who discovered Hooke's law?

Hooke's law was first stated by English scientist Robert Hooke in 1660. However, it wasn't until 1676 that he published his findings in his book "Lectures de Potentia Restitutiva".

## 3. What is the mathematical equation for Hooke's law?

The mathematical equation for Hooke's law is F = -kx, where F is the applied force, k is the spring constant, and x is the displacement of the object from its equilibrium position.

## 4. How is Hooke's law used in real life?

Hooke's law is used in many real-life applications, such as in the design of springs, shock absorbers, and elastic materials. It is also used in fields such as engineering, architecture, and biomechanics to calculate the stress and strain of materials.

## 5. What happens if the force applied exceeds the elastic limit of an object?

If the force applied to an object exceeds its elastic limit, the object will no longer follow Hooke's law and will experience permanent deformation. This means that even after the force is removed, the object will not return to its original shape or size.