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Hooke's law: What is a Hooke spring?

Important Formula

What do the formula symbols mean?

Restoring force

Unit
Spring force exerted by the spring to return the spring to its unstretched state.

The minus sign takes into account the direction of the force. The force acts against the direction of deflection. For the magnitude, the minus sign may of course be omitted.

Spring constant

Unit
The spring constant is a material constant and depends on the spring used. It tells how well the spring can be stretched (that is how elastic the spring is).

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)2.06

Deflection

Unit
The deflection of the spring from its neutral position. For example, if you pull on the spring, $$y$$ is the distance by which the spring was deflected.

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:

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:

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: