410 



BELL SYSTEM TECHNICAL JOURNAL 



The radian frequency of the acceleration is 



TT 



0}2 — — 



7"2 



COO 



and this is to be compared with the frequency 



W2 



that would obtain if the cushioning were linear with spring rate ^o • The 

 ratio coo/co2 (i.e., t^/tq) was obtained by numerical integration of (2.9.3) 



= - = 4/- 



To \ t 



2.0 



3.0 



Fig. 2.9.1- 



do 



-Duration of acceleration pulse for cushioning with tangent elasticity, 

 equation (2.9.3). 



See 



and is plotted in Fig. 2.9.1 against the ratio dhld^. The figure shows that 

 for Jb/Jo < 1, the pulse duration varies almost linearly with t/fc/Jo • As the 

 bottoming distance becomes larger than that required for Unear cushioning 

 with spring rate ^0 , the pulse duration approaches asymptotically the 

 duration tt/wq for the linear case. 



As Jfc/Jo decreases, the pulse duration becomes shorter, but the maximum 

 acceleration increases, in accordance with equation (1.9.4) and Fig. 1.9.1. 

 The shapes of the acceleration-time curves for several values of Ji/Jo are 

 illustrated in Fig. 2.9.2. They are more sharply peaked than the corre- 

 sponding curves for cubic elasticity (Fig. 2.8.2) as might be expected from 



