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BELL SYSTEM TECHNICAL JOURNAL 



t 





with the equation relating time and velocity, 



dx; 



we find 



~2g Jo 



t = 



y4^ 



- Pdxi 



(2.12.1) 



(2.12.2) 



As an example, consider the problem of a 15-pound article supported on 

 cushioning with the load-displacement curve shown in Fig. 2.12.1. The 

 package is to be dropped from a height of 3 feet. The computations are 



X2 



Gog 



4 



Fig. 2.11.2 — -Acceleration-time curves for cushioning with hyperbolic tangent elasticity. 



given in detail in Tables III and IV. The headings of Columns (1) to (8) 

 of Table III are the same as in Table II, Section 1.15. An is the integral 

 under the radical of equation (2.12.2). Column (10) of Table III is the 

 integrand of Equation (2.12.2), i.e., it is proportional to the reciprocal 

 of the velocity expressed as a function of displacement. The function 

 is plotted in Fig. 2.12.2 and its integration is performed in Table IV. In 

 columns (11), (12) and (13), intervals of Xi are chosen to suit the shape of 

 the curve. The values for column (14) are taken from column (10). Col- 

 umns (15) and (16) perform the same operations on the integrand 

 (y\l^h — Ariy that are performed in Columns (5) and (6) of Table III on 

 the integrand P. 



