682 



BELL SYSTEM TECHNICAL JOURNAL 



0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 2.4 2.6 2.8 3.0 3.2 

 CIRCULAR DISPLACEMENT - 9q 



Fig. 14 — Transient acceleration during initial part of triangular whip. 



Letting 



and 





= \ 



Vy 



(iit = 



= CO Vl 



,2 = 



CO7 



Substituting 



in which 



X = sin (X^o + lA) 



7 



(45) 



tan \p = 



'7/7 



1 - 2rf 



Figure 14 is a plot of X against ^o for various values of r;. It is noted that 

 for 7] — .5 of critical damping the initial acceleration is equal to the un- 

 damped, X being one. 



The data presented here are also applicable to long duration pulses, be- 

 cause the final results have been given in dimensionless quantities, the units 

 of measurement being those of the pulse. 



Symbols Used 



Mass m 



Mass of base nn 



Spring stiffness k 



