DYNAMICS OF PACKAGE CUSHIONING 443 



.2 



Ao = 7=- VA^ + B' sin (coi/,„ + r? - coi/^) 



coo V 2g/i 



1 . / , , . -i4\ (3.7, 



v-2 Sin I Wo /m — coo /a — Sin -y J , 

 coo\ \ rfo/ 



3) 



ts < t < 2t, 

 where 



OJo 



Wo \/2g/; ' . _ /^Y \wo ^0/ 



\"i/ 



Wo 



Wo 



— 7^=^ -5 = 3 — ^„ 2-S/4/1 rf — COS I — sin - ) 



V2gh ^ _ /cOoV L "0 y ti^ Vc^O ^O/ J 



T? = tan - 



and tm is the root of 



.3 



w 



Wo \/2g^ 



7^^. VA^ + ^2 cos (w]/,„ + rj - wi/,) 



1 / 



-fe) 



cos I Wo tm — 0)0 is — Sin 



-1:)=» 



that yields the largest value of Ao in equation (3.7.3). Region 3 is gov- 

 erned by 



X + wix = (3.7.4) 



and the initial conditions are the terminal conditions of Region 2. By 

 the same method as was used in Section 3.2, we find 



Ao = ^^¥^ \h) 4/1 - I - cos h sin- f)] , 



1 L\'«^o/ V dl \wo do/ A (3.7.5) 



\Wo/ 



t> 2ts. 



The largest value of Ao from equations (3.7.1), (3.7.3) and (3.7.5) is 

 plotted against wi/wo in Fig. 3.7.2 for several values of d^/do . 



