dæmpningskonstant

The damping constant, often denoted by the Greek letter zeta (ζ), is a parameter used in the field of engineering and physics to describe the damping ratio of a system. It is a dimensionless quantity that quantifies the amount of damping present in a system, which is the resistance to motion. The damping ratio is defined as the ratio of the actual damping in a system to the critical damping, which is the minimum amount of damping required to prevent oscillation.

In the context of mechanical systems, the damping constant is used in the differential equation that describes the motion of a damped harmonic oscillator. This equation is given by:

m * d²x/dt² + c * dx/dt + k * x = 0

where m is the mass, c is the damping coefficient, k is the spring constant, and x is the displacement. The damping constant ζ is related to the damping coefficient c by the equation:

ζ = c / (2 * sqrt(m * k))

A damping ratio of 0 indicates no damping, while a damping ratio of 1 indicates critical damping, where the system returns to equilibrium as quickly as possible without oscillating. A damping ratio greater than 1 indicates overdamping, where the system returns to equilibrium without oscillating, but more slowly than in the critically damped case. A damping ratio between 0 and 1 indicates underdamping, where the system oscillates with decreasing amplitude until it comes to rest.