672 



BELL SYSTEM TECHNICAL JOURNAL 



The steady state after the transient is (from Eq. 21) 



'" ly^ - 1) V 



COS llTlpT — (p COS llTT 



- COS 2ir(p{T - 1) + <p' cos 27r(r ^ 1)) 



which reduces to 



ba = 7 i, sin {liTipT — TZip). 



1 — <p^ 



(23) 



0.5 



1.0 



1.5 2.0 2.5 3.0 



PULSE LENGTH (INTERVAL) 



3.5 



Fig. 7- 



NATURAL PERIOD OF SYSTEM 



-Maximum amplitude as a function of frequency ration-steady state sine whip. 



The maximum ampUtude is 



A = 



sm -Kip 



(24) 



a plot of which is shown in Fig. 9. 



Practical Considerations 



Let us now consider the action of these various whips in terms of what 

 they do to the system. The designer of shockmounts is primarily interested 

 in the displacement across the mount or the relative displacement of base 

 and mass. 



In Fig. 10 the relative transient displacements for four systems are shown 

 when subjected to a triangular whip. The natural frequencies are .4, 1.0, 

 1.5, and 2 times the frequency of the whip. From this it appears that the 

 maximum relative displacement is approximately equal to the maximum 



