DYNAMICS OF PACKAGE CUSHIONING 429 



To find the corresponding quantity for the package drop, first find the 

 cushion frequency: 



/ 1 . /^ 1 . /3300 X 386 „ 

 2ir \ mi 2ir y 10 



The ratio of the element frequency to the package frequency is therefore 



Ti ^ coi ^ 120 ^ 2 1 



/a 0)2 57 



Entering Fig. 3.2.2 with coi/a)2 = 2.1 we read, from the curve 0i = 0.01, 

 Am = 1.59. The 199g acceleration pulse in the package drop is therefore 

 equivalent to a slowly applied acceleration of Ge = 199 X 1.59 = 316g. 

 This is almost 40% in excess of the value (228g) found to be safe from the 

 shock machine data. The cushioning is therefore judged to be inadequate. 

 Ine procedure for finding the correct spring rate for the cushioning is as 

 follows. It is known that we must have 



Therefore, take 



Now 



Therefore 



Also 



Ge < Gi 



Ge = AmGm = 228. 





Amf^i = 409 rad/sec. 



;i = 27r X 120 = 754 rad/sec. 



Then, with successive trial values of W2 , we calculate wi/coo , enter Fig. 3.2.2, 

 read the corresponding value of Am from curve ^i = 0.01 and test to see if 

 the product AmUi = 409. The combination which satisfies the test is found 

 to be 



0)2 = 280 rad/sec. 



cci/iOi = 2.69 



Am = 1.47. 



