TRANSIENTS IN MECHANICAL SYSTEMS 

 Equation (32) may now be expressed as 



679 



in which 



and 



5a = — V{A' + J52) sin (^7/ - 0) at > 2r)Tr(p (33) 

 ir<p 



tame = ?■ 

 A 



^ = -1 + le'^" cos 7r<py - e'"'"' cos lircpy 

 B = 2^^" sin 7r<py - e"^^ sin livipy 



(34) 

 (35) 



0.8 



a. 0.4 



0.5 



1.0 



.5 2.0 2.5 3.0 



PULSE LENGTH (INTERVAL) 



3.5 4.0 



4.5 



NATURAL PERIOD OF SYSTEM 



Fig. 13 — Effect of damping on steady state amplitude for triangular whip. 

 From equation {^3) we obtain the maximum displacement 





at > 2'r]'K<p 



in which 



5.0 



(36) 



at — -\ tan ^ - + tan ^ — ) at > ^-q-Kip 



7 \ ?7 AJ 



In Fig. 13 a plot of equation (36) is shown for t; = .5. This indicates that 

 the peak value of A is .24 as compared to 1.48 when no damping is present. 



Accelerations 



The transient accelerations of the mass m during the whip action and the 

 subsequent steady state may be found by examining the acceleration during 

 the first part of a triangular whip. Designating the velocity of displacement 



