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BELL SYSTEM TECHNICAL JOURNAL 



were equal to zero (see Fig. 2.5.3). The second factor (of nearly two) is 

 due to the fact that the maximum acceleration is reached at time / = 

 when /32 = 1 (see Fig. 2.5.2) and the response of an almost undamped sys- 

 tem (/3i = 0.005) to a suddenly applied and subsequently maintained 

 acceleration is double the response to a slowly applied acceleration (see 

 curve (a) Fig. 3.8.1). For /3i > and /32 < 1 the amplification factor is 

 less than four, as 051/0)2 — ^ <» , in accordance with the curves plotted in Fig. 

 3.5.8. 



Example: A 1.5-pound vacuum tube is to be packed in a container whose 

 estimated weight will be at least 50 pounds. The cathode structure of the 

 tube has a natural frequency of 25 c.p.s. with damping 0.5% of critical 



33 



\W 2 



Fig. 3.5.7 — Amplification factors for linear damped cushioning with no rebound. 

 i32 = 1.0. See equations (3.5.1) and (3.5.2). 



and its safe acceleration, as determined in a centrifuge, is 90g. What 

 spring rate of cushioning is suitable for protecting the cathode in a drop of 

 five feet? It is specified that the cushioning shall have damping 50% of 

 critical. 



Assuming linear cushioning, the spring rate that would be prescribed, by 

 considering maximum acceleration alone, is 



ife2 = 



W^GL 1.5 X (90)' 



= lOllbs./in. 



2h 2 X 60 



Considering damping, Fig. 2.5.3 shows that 50% of critical damping does 



