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BELL SYSTEM TECHNICAL JOURNAL 



Then 



4 = 



Xat 



2 — COS -- 



C02 ZC02 



(■ ' -■) 



(3.2.13) 



We find, on comparing (3.2.13) with (3.2.9) that for coi < wo equation 

 (3.2.13) gives the larger value of .1,,,, while for coi > wo equation (3.2.9) 



1.8 



1.6 



I 

 '^' 1.4 



1.0 



r' .6 



.4 



10 



^'/^ 



^u' 



Fig. 3.2.2 — Amplification factors for linear undamped cushioning with perfect rebound. 

 See Fig. 3.2.1 and equations (3.2.9) and (3.2.13). 



gives the larger value of Am. That is, when the duration of impact is 

 shorter than the half-period of vibration of the element, the maximum 

 displacement (and stress) in the element occurs after the impact is over. 



The curve marked ^Si = in Fig. 3.2.2 is a plot of the largest value of Am 

 from (3.2.9) and (3.2.13) with the frequency ratiocoi/co2 as abscissa. (3.2.13) 

 was used for aji/co2 ^ 1 and (3.2.9) for co 1/0)2 ^ 1. The maximum value 

 of Arr, is 1.76 and occurs at co]/c<;2 = 1.6. Hence, at this frequency ratio, the 

 deformation of the element is 1.76 times as great as would be expected from 

 a calculation using the maximum value of acceleration alone as in Part I. 



