922 
Be Exponential Decay with Cut-Off. 
t/ 
a) 
F(t) =Fe - -t,/@ 
Ont) Fe 
Substituting into Eq. (I-5)- and following the development of Eqe (I-27): 
2 
x = = sin wt © cos ot + 7t/0 H(t) 
M(1 + a” 0%) | 00 
(I-3la) 
t=t 
2 .-t,/0 -—2 
~ 2P S| 2 sin w(t = ty) - cos w(t -t,) +e © | H(t - t) 
M(1 + a” 9”) | 2 
Fort, << t < t, , Ea (I-3la) becomes 
F 9 1 27% /e 
xs re — sin wt ~ cos wt - sin w(t - t,) 
M(1 + w” 9”) | 20 
(I-31b) 
-t_/9 
+8 of cos w(t - | 
Differentiating Eq-e (I-3lb), and solving for the time of maximum deformation: 
-t,/@ -t,/e 
ee o/ cos wt, + wes o/ sin ot 
9 (I-Slc) 
ate: 
sin at, + wOs cos at, - 00 
Setting the numerator and denominator of Eq-e (I=-3lc) equal to a and b respec- 
tively, and performing a trigonometric substitution: 
=107= 
