Let 



AE 



3J 



then Equation [2] becomes 



da 2 a 3 ^t 2 



(4] 



v;hlch Is the equation' of longitudinal wave notion. Also, the 

 tensile force acting on the cable can be written a3 



2 i 

 dT = AE — ^ d3 + u. g sin 9 d3 



ds 2 



[5] 



Integration of Equation [3] yields 



T = AE — l + p. g s sin + constant 



33 



[6] 



If the tension at the lower end of the cable is denoted by To 

 when the cable is In equilibrium.. I.e., when d^/cs = 0, Equation 

 [6] becomes 



d£ 



T = T + (i g 3 sin Q + AE ■p 



[7; 



By the method of separation of variables, a solution of 

 Equation [h] can be written as 



£(a,t) = (C x cos cut + C 2 sin cot) (C 3 cos % s + C 4 sin 3 s) [8] 



