186
Appendix H
The corresponding electrical, Z e , and mechanical, Z m , impedances for both systems
are:
Z e = R + i
L
ω
ω
2
− ω
2
0e
(H.5)
Z m = b + i
m
ω
ω
2
− ω
2
0m
(H.6)
where i is the imaginary unit, ω 0e = (1/LC)
1/2 and ω 0m = (k/m)
1/2 are the
corresponding resonance frequencies of both systems.
The corresponding susceptibities, α(ω) = i/ωZ(ω), are:
α e (ω) =
ω 2 − ω 2
0e
+ iωγ e
L
ω 2 − ω 2
0e
2 + (ωγ e )
2
(H.7)
α m (ω) =
ω 2 − ω 2
0m
+ iωγ m
m
ω 2 − ω 2
0m
2 + (ωγ m )
2
(H.8)
where γ e = R/L and γ m = b/m are respectively the electrical and mechanical
damping factors or resonance widths.