s(w) = — | x. (oe ews ds 
220 
2 2 
1 
_ Ge, oer oe si ae (6.48) 
2x agtiwof 2 ap+@ 
Re {- } showing to take the real part of a function {-}. 
If we express 
(D+ ao) = aD), 
then 
s(@)=—4 —, (6.49) 
which is again a form similar to Eq. 5.50 for the discrete process. 
63.2 Correspondence of A(2) to ARMA(2.1) 
Generally for a damped mass spring linear vibrating system, the second order differ- 
ential equation as 
MX(t) + BX(t) + KX(t) = fit) (6.50) 
stands as its fundamental formulation, where f(r) represents the forcing function. 
Here 
M = mass 
B = damping coefficient (linear to the velocity) 
K = restoring coefficient (linear to the displacement). 
Transforming Eq. 6.50 by conventional expressions as 
B 
B Wag 28 
— = 2K0),, k= - — = 
M or 2 Gis Oe! (6.51) 
Ko re K 
Wie ns M 
gives 
x) +20 ! x) +a2X(1) = Re) (6.52) 
dt " dt Mi 
213 
