# Hooke's law: What is a Hooke spring?

## Important Formula

## What do the formula symbols mean?

## Restoring force

`$$ \class{red}{F} $$`Unit

`$$ \mathrm{m} $$`

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

`$$ D $$`Unit

`$$ \frac{\mathrm{kg}}{\mathrm{s}^2} $$`

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

`$$ y $$`Unit

`$$ \mathrm{m} $$`

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: