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:
Here, \( D \) is a spring constant that indicates how elastic a 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) „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:
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.