Degree of damping

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The degree of attenuation , also damping or Lehrsches attenuation (by Ernst teaching ), common symbols is, in the physics a measure of the damping of an oscillatory system. It is a quantity in the number dimension . It can be read from it how the system behaves after a stimulus .


The differential equation of a linear damped oscillator can be given the following form, regardless of the physical background of the oscillation system:

There are:

  • : Degree of damping
  • : Natural angular frequency of the undamped system

Mechanical systems

For a spring / mass oscillator, Lehr's damping is calculated as follows:

There are:

: Damping constant
: Spring constant or spring stiffness
: Mass

The characteristic frequency corresponds to the natural frequency of the undamped system and is here .

Based on the usage in English, the degree of damping can be understood as the ratio of the damping constant to the critical damping constant . This means

The critical damping constant is the damping that is necessary to achieve the aperiodic limit case .

Electrical systems

The following applies to electrical oscillating circuits (see quality factor )

for the series resonant circuit: for the parallel resonant circuit:

Are there

: Resistance
: Capacity
: Inductance

Analysis of stability

The degree of damping can be used to characterize the vibration behavior. For this one considers the solution of the characteristic polynomial of the differential equation:

A distinction is now made depending on the size of the degree of damping:

  • : unstable - upward swinging system
  • : undamped, borderline stable - continuous oscillation with constant amplitude
  • : damped oscillation (case of weak damping)
  • : aperiodic borderline case - precisely no overshoot (case of critical damping)
  • : aperiodic solution - not oscillating (asymptotic approach to the center of oscillation for , creep case)

Other attenuation dimensions

Logarithmic decrement

The degree of damping describes the vibration behavior of an entire physical system. It is directly related to the logarithmic decrement via the equation:

This quantity can also be found as a logarithmic attenuation measure in dB.

Attenuation level in acoustics

In the case of a plane wave, the attenuation measure with the symbol is the logarithmic ratio of the amplitudes of a field size (e.g. sound pressure) at two points lying one behind the other in the direction of sound propagation; (DIN 1320).

Attenuation in electrical engineering

In electrical engineering, the damping behavior of resonant circuits is indicated by the quality factor . The relationship between the quality factor and the degree of damping applies:


  • Michael M. Rieländer: Real Lexicon of Acoustics. Erwin Bochinsky publishing house, Frankfurt am Main 1982, ISBN 3-920112-84-9