DYNAMICS OF PACKAGE Cl\SHIO\IXG 



431 



It may be observed that (3.4.7) is independent of the properties of the 

 cushioning. Hence, as long as (3.4.2) is satisfied, any cushioning at all 

 may be used for an element that satisfies (3.4.7) regardless of the magnitude 

 of the maximum acceleration G,„ . In particular, rigid mounting is suitable 

 for such an element. The only precaution to be observed is that the maxi- 

 mum acceleration and duration must not be unfavorable for other elements 

 of the packaged article. 



Example: A 9-pound vacuum tube has an anode structure for which the 

 safe maximum acceleration is 200g as determined in a centrifuge test. 

 The natural vibration frequency of the anode is 35 cycles per second and the 

 damping is 1% of critical. What cushioning around the tube is required to 

 protect the anode from damage in a package drop of 3 feet? 



Calculate 



I.IG, 1.1 X 200 



Vh 



VS6 



= 36.7 c.p.s. 



This is greater than /i = 35 c.p.s and hence any cushioning is safe for the 

 anode. The results of calculations for cushioning with spring rates of 50, 

 500, 5000, 5 X 10 and 5 X 10 pounds per inch are given in the following 

 table : 



In each case the product of AmGm is less than the allowable 200 and, as long 

 as the combination of Gm and the amplification factors for other elements 

 does not exceed the allowable AmGm for those elements, the cushioning is 

 suitable. The precaution to observ^e is that higher-frequency elements 

 shall not have amplification factors such that A,nGm may be excessive for 

 them. 



3.5 Amplification Factors for Damped Sinusoidal Acceleration 



If the outer container of the package is heavy enough (see Section 2.3) 

 there will be no rebound and the packaged item will vibrate in the cushion- 

 ing after impact. For linear cushioning with velocity damping, the accelera- 

 tion produced by the vibration will be a damped sinusoid (equation (2.5.5) 

 and Fig. 2.5.2). The system to be considered is shown in Fig. 3.5.1. 

 To determine the efifect of the damped vibration of Wo on the mass nii , 



