Fig. 12.2. Displacement—force relation of set-up spring. 
as are shown in Figs. 12.3 and 12.4. Hereo, is the standard variation of the linear system 
a 
when € = 0. These figures show that the probability distribution of extreme p, mi 
x 
varies considerably with the extent of nonlinearity, expressed by the value of e€. 
Fig. 12.3. Probability distribution density of the extreme (peak) 
values of Duffing type oscillator. 
(From Crandall.®4) 
341 
