dt 2 



3=0 



= [M g 3ln - T] 



s=0 



26; 



but from Equation [7l 



T = T + AE 



•s 1 



03 



[27 J 



Hence, the boundary condition given by Equation [26] becomes 



af£| 

 at 2 ! 



.r« 



;=o L 



g sin - T - AE 



an 



[28] 



However, it is recognized that the steady-state tension must 

 be the same as the weight of the cable and body. Therefore 



H g sin 9 - T = 



[29] 



Hence, Equation [28] becomes 



d 2 £(0,t) = _ AE b'c,(0, t) 

 dt 2 M ds 



30] 



The displacement Is assumed to be zero at t = 0, as in the 

 previous section. Hence the displacement can be written as 



£(s,t) = sin cut (C^. cos - s + C sin ^ s) [31] 



Applying tne boundary condition at s = 0, which is given by 

 Equation [30 ] to Equation [31] yields 



% AE ^S 



[32; 



