TRANSIENTS IN MECHANICAL SYSTEMS 



669 



From 1.04 



F{s) = 



aojo 



S -\- CCq 



Substituting (13) in (5) we obtain 



(1 + €-"""'). 



X{s) = 



(Kjl'jjf) 



(j + U )(S + Uo) 



(1 + ,-"'"«). 



(13) 



(14) 



<J 1.6 



0.5 1.0 



1.5 2.0 2.5 3.0 3.5 4.0 4.5 



PULSE LENGTH (INTERVAL) 



NATURAL PERIOD OF SYSTEM 



= ^ 



Fig. 5 — Maximum amplitude as a function of frequency ratio-steady state tri- 

 angular whip. 



The inverse transform gives us 



aco^o)o r/1 



X = -2 2 I ~ SI 



sm coq/ — ~ sin (at 



/ V^o 



sin 0)0 (t — ~) 



coo 



- sin CO (/ - -) ) u (t - -)\ (15) 



CO coo / COo J 



and dividing this into two parts again, the transient and the steady state, 

 wp find for the transient, 



aco-coo fl . 1 . "I 



X = -2 2 ~" sm COo/ — ~ sm o)t 



CO — COo L^o " J 



and substituting the dimensionless quantities 



t/. 



COo 



= <p 



and 



ir/coo 



we find 



- V ( 

 V - 1 \ 



sin TTT — — sin 2ir^T 

 2(p 



y 



(16) 



