925 
4s a@tp5 —»0, *— 1, 
where ¥ is the response relative to step response. 
¥— > 1/2- A plot 
i-e-, approaches step response as expected. As at, —— > 00, 
of & vs- wt, is given in Fig. I-7. 
9- Successive Step Functions Fy Lt Fy +AFe= Fy 
| 
F(t) = Fy H(t) + AF H(t - t,) (I-39) 
F 
= eee ae) ee ma H(t = to) (1-40) 
x= 
Dy? + w® M D,® + a 
Following the development leading from Eqe (I=8) to Eqe (I-99), the solution 
to Eqe (I-40) is: 
F 
—e = (1 = cos wt) H(t) + af [2 = cos a(t - to)| H(t = to) (I-41) 
Ifto<-, then for t > to : 
x= ph - ae cos wt + oF aF (cos @t cos ot, + sin ot sin wt,) 
k k k k 
x72 2/7 + AF cos wt, cos ot - SF sin aot, sin ot (I~42) 
k k k k 
= AF ein wt, cos at (I-43) 
x == (¥, + AF cos wt.) sin ot - F 
For maximm deformation: 
F sin ot 
tan ot, = ee 
Fy + A¥ cos ato 
-110- 
