and Equation [12] becomes 



:-.(s,0) •-= C s a.ln | 3 = 



[II] 



Therefore, C^ s 0. With thla result, Equation [12] can be 

 rewritten a 3 



;(s,t) a C 6 aln .,>t sin a 



[15) 



If the upper end of the cable, a - ;, Is displaced according 

 to 



f,(i!,t) a p aln t ot 

 Equation [15] becomes 



Hence 



p sin (i)t « C sin cot sin 



B_ 



CD,? 



<> sin <"£ 

 a 



and Equation [15] can now be written as 



£(3,t) « ~T' (iTj; aln cot sin 



[16] 



[17] 



[IS] 



[191 



Equation [19] specifies the space and tine behavi'or of the 

 longitudinal displacement of Uw cable. 



Let 



AT = AE ^ 



Then Equation [7] can bi written at s = aa 



T « T Q + AT J , 



[20] 



[21 i 



