INPUT a, 
: HU hi 
: H | | ! A uy 
ee MM ied 
Be Rae 
OUTPUT X, 
8.00 
SS 
SS 
00.08 0.00 
0.00 100.00 200.00 300.00 400.00 500.00 600.00 700.00 800.00 900.00 1000.00 
Fig. 13.4. X,=(1.5+ 0.286%) X1—0.96X,0+4:, 
Input a, = sin{sinz Kt): 4; f(t) is increasing by time. 
(From Ozaki.98) 
In Eq. 13.50, the coefficients 1,2, 01,72 are to be chosen to make the damping 
coefficient negative, when the amplitude X;_, is small and the oscillation starts to diverge, 
and to make the damping coefficient positive, when the amplitude X;,_, is large and the 
oscillation starts to decay. Mathematically 
A? -~(b1 + 1)A—- (G2 + M2) = 0, (13.51) 
has roots outside the unit circle, and 
1° -oA-$2=0 (13.52) 
has roots inside the unit circle, as shown schematically in Fig. 13.6 
387 
