The four constants, C x , C 2 , C3, and C 4j nust be determined 

 from the boundary and Initial conditions of the specific 

 problem. 



SPECIFIC SOLUTIONS 



Two basic types of problems, differing only in the end 

 conditions are investigated. Cne end of the cable system is 

 disturbed by a simple harmonic displacement while the ether 

 end is fixed or allowed to move. The cable-anchor configuration 

 Is assumed to be a straight line inclined to the horizontal. 

 Also, as previously stated, the weight of the cable Is considered 

 in the determination of the equilibrium tension and the hydro- 

 dynamic forces are neglected. 



LOWER END RIGIDLY FIXED 



In this case, the origin of the coordinate system is placed- 

 at the fixed lower e: 1. Then, the boundary condition at thi3 

 point can be written as 



e(o,t) = [9] 



and Equation [8] becomes 



£(0,t) - C 3 {0 X cos ay; v C 2 sin cut) = [10] 



Equation [10] can be satisfied for all values of t only If 

 C 3 = 0, Hence, Equation [8] can be written as 



£(s,t) = C-i sin g s (C x cos tot f C 2 sin tot) [11] 



\ 



i 



£(s,t) = sin 3 s (C, cos xt + C fc sin tot) [12] 

 If the system is at rest at t - 0, then 



5(a,0) = [13] 



