Where c is the propagating velocity of the wave, [eta] is the viscous damping constant
for the current media the wave is traveling in, and |r - [r.
9] suggested that the radiation damping constant
in the zeropoint field as [[GAMMA].
Jankowski  puts forward a nonlinear viscoelastic model based on the Hertz impact model and then derived the expression of the damping constant
of the nonlinear viscoelastic impact model.
1) which introduces the relationship between the bending moment (M (x,t)) and deflected shape (w(x,t)) of the beam, equivalent flexural stiffness and damping constant
of the beam is extracted:
where n is the damping constant
, which indicates the growth rate of losses with the increasing distance d.
The displacement of the pendulum head ([theta](t)) is evaluated as a function of time with a damping constant
[lamda] using equation 3.
The damping constant
[GAMMA] will be assumed small compared to [[omega].
If additionally the oscillating mass were immersed in a viscous medium with damping constant
b, the oscillator would experiment a force opposed to its velocity, and the equation above would become
corresponding to a non-linear oscillator (a pendulum) immersed in a dissipative medium of damping constant
b and which is connected to an external applied sinusoidal force Fo oscillating with frequency [OMEGA], the free angular frequency of the linear oscillator is [[omega].
S], D) of forced acceleration of an oscillator with small damping constant
D, usually D = 0.
The loss of energy in each cycle, [DELTA]W, was calculated from the hysteresis loop, and the damping constant
, [beta], calculated from [DELTA]W as follows:
For example, changing the value of the partial frequencies alters the perceived length of the bar, whereas changing the damping constant
results in a perceived change of material.