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BELL SYSTEM TECHNICAL JOURNAL 



Equation (1.9.2) can then be substituted into (1.4.3) to obtain the maximum 

 force Pm in accordance with (1.2.17): 



2^0 ^6 . / (ir^W^hX 



- 1. 



(1.9.3) 



do 



Fig. 1.9.1 — Curve for finding maximum acceleration for cushioning with tangent elasticit_v. 



See equation (1.9.4). 



The maximum acceleration is then obtained from (1.2.16) and may be 

 written in the form 



Gm 



Go 



2d, 



TTch 



/ 



firdoY 



1 



(1.9.4) 



where do and Go are defined just as in (1.5.2) and (1.5.5). Go is the maxi- 

 mum acceleration that would obtain if the cushioning did not bottom, that 

 is, if the spring rate remained constant at its initial value ^o • do is the 

 maximum displacement that would be reached under the same linear con- 

 ditions. Hence Gm/Go is a multiplying factor to be applied to a hypothetical 

 linear cushioning to take into account the effect of bottoming. The multi- 

 plying factor depends only on the ratio (db/do) of the amount of space 

 actually available to the amount of space that would be used under linear 

 conditions. 



