# Critical Damping Coefficient (related to the natural frequency)

## Description

A harmonic oscillator is a system that, when displaced from its equilibrium position, experiences a restoring force, proportional to the displacement. If a frictional force (damping) proportional to the velocity is also present, the harmonic oscillator is described as a damped oscillator. If the system contained high losses is called overdamped. Commonly, the mass tends to overshoot its starting position, and then return, overshooting again. With each overshoot, some energy in the system is dissipated, and the oscillations die towards zero. This case is called underdamped. Between the overdamped and underdamped cases, there exists a certain level of damping at which the system will just fail to overshoot and will not make a single oscillation. This case is called critical damping. The key difference between critical damping and overdamping is that, in critical damping, the system returns to equilibrium in the minimum amount of time. The Critical Damping Coefficient is depended on the natural frequency of the simple harmonic oscillator.

Related formulas## Variables

c_{c} | Critical Damping Coefficient (N*s/m) |

m | The mass of the body (kg) |

f_{n} | The natural frequency of the simple harmonic oscillator (hz) |

π | pi |