Therefore, Equation [31] becomes 



, . r to ato , in 1 



f(s,t] = C r sin cot cos r- s + — sin r- 3 



[33] 



As in the previous section, the upper end of the cablf 

 i3 displaced according to 



= I, 



il(i,t) = p sin tot 



fl-i] 



Hence 



cos u>± + ?1^ sin 

 a AE 



[34] 



and now the equation prescribing the space and time behavior 

 of the cable can be written as 



5(s,t) = 



p 



floi 



3 sin tot r 



I + Sl^ sin^A L 

 AE a 



cd ■ aMto . cd "1 

 cos — s + -77T sin — s 



a J 



AE 



[35] 



Therefore, the change in the dynamic tension with respect tc 

 the static tension at the upper end can be written as 



and 



T s=0 = ^o + ^|s=0 

 T u T u T u 



h^l = 1" + AT| a=J j 



T u 



[36] 



[37] 



where 



Afr , AT , 2i AE p 5- sin Mt [aMto coa , (03 1 r ~ , 



AT = AE r 1 = -i a -rr- — rrr -r^r cos - sin f ~>£ \ 



03 cos _i. + d f lCJ sin E£ Ah. a a lj<- 1 



a AE a J 



