Alexander Fufaev
My name is Alexander FufaeV and here I write about:

Hooke's law: What is a Hooke spring?

A Hooke spring is an elastic mechanical spring that builds up a restoring force \( F \) when it is stretched or compressed. The restoring force of a Hooke spring depends on the deflection \( y \).

In Hooke's law, the force \(F \) and the deflection \(y\) are linearly related. This means: If you double the deflection of the spring, the restoring force \(F\) doubles:

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Force ( magnitude) - Hooke's law
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Here, \( D \) is a spring constant that indicates how elastic a spring is.

Table : Examples of spring constants for different materials
Material Spring constant \(D\) in \(\frac{\mathrm N}{ \mathrm{m} } \)
Aluminium (Al)0.81
Aurium (Au) „Gold“0.92
Titanium (Ti)1.45
Platinium (Pt) „Platin“2.06

Hooke Spring = Harmonic Oscillator

Hooke's spring is an example of a harmonic oscillator. The mass on the spring performs harmonic oscillations and can be described with a cosine or sine function:

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Deflection of the spring pendulum as a function of time
y(t) ~=~ x_0 \, \cos(\omega \, t ~+~ \varphi)
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The restoring force \( F \) is proportional to the deflection \(y\), whereby the propotionality constant is the product of the mass \(m\) and the frequency \( \omega \) with which the spring oscillates:

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Restoring force as a function of time
F(t) ~=~ m \, a(t) ~=~ -m \, \omega^2 \, y(t)
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1
0
1
0
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0
1
0
1
0
1
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How to measure mechanical forces?

A mechanical force \( F \) can be measured with a Hooke's spring. The change in length \( y \) of a Hooke spring is measured. If you know the spring constant \( D \), you can easily calculate the force using Hooke's law.