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BELL SYSTEM TECHNICAL JOURNAL 



The acceleration pulse will then look like the curve marked kb/ko — > <» 

 in Fig. 2.10.1. 



There will be three regions in which to consider the relative displacement x: 



Region 1 < / < /, 



Region 2 ts < t < Its 



Region 3 t > 2ts 



The relative displacement {x = Xi — X2) of Wi with respect to W2 will have 



//////// 



Fig. 3.7.1 — Idealized system representing abrupt bottoming. 



the same functional form for Region 1 as in the linear case (see equation 

 (3,2.6)), and the amplification factor is, by analogy with (3.2.9), 



OJo 



Int 



sm 



COo 



- 1 



COo 



< / < /, , 



(3.7.1) 



+ 1 



where 



COo = k(j/m2 



For Region 2, we use the differential equation 



X -^ wix = coo\/2gh sin coo(^ — 2ta) 



(3.7.2) 



and, as initial conditions at ^ = /« , we use the terminal conditions for 

 Region 1 with the sign of [x2]«=«s reversed. The amplification factor for 

 this region is found to be (by the same method as in Section 3.2): 



