1 , 
hg mT) = aS | Hg yn) Cate (10.27) 
Frequency response Hg ,(@) is easily obtained by Eq. 10.25. 
Then, when the nonlinear damping term is shifted to the right-hand side of Eq. 
10.24 and ¢o is used in the nonlinear term, the first approximation $, is expressed by 
$1 + 2ab) + wi. = mt) —Bipoldo. (10.28) 
As the left-hand side of Eq. 10.28 is in the same form with that of Eq. 10.25, using 
hgom(T) as the impulse response function gives 
gi= | hgom(t—K)|m(L) —Blbow)ipow)} du, (10.29) 
= go(t)-¢1 (0). (10.29”) 
Since a and are small, the convergence of this approximation is assumed. Then, the 
correlation function is 
Ro.9,0) = El{Pole + 1) - 91 (t+ D{Golt) - $1 @} *] 
(* Shows the conjugate) 
= Elpolt + tpd'(t)] — 2 Re {Elpile + 1)1(0)) } + ElGie + HG 1* 1, 
(10.30) 
here Re { - } indicates to take the real part of a function {-}. 
The spectrum is manipulated by taking the Fourier transformation of Rg,g,(T), 
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