Figure 6 is an example of the time variation of m- 



at the upper end of the 6000-foot configuration with the lower 

 end fixed. This curve was computed from Equation [25] for a 

 circular frequency, co, of 1.0. 



NATURAL FREQUENCIES 



The natural frequency is defined as the frequency which 

 causes AT -> ». Hence, for the fixed end case which is given 

 by Equation [25], AT -> » y:hen sin coi/a -> 0. Therefore 



o> n => -j- where n = 1, 2, 3, . . . . [39] 



If the lower end is free to move AT -* » when 



a»i al'ico , tot , , , 



cos 'a - + TE" 3in a "* ° ^°^ 



as can be seen from Equation [3&] Equation [*t0] can be 

 written as 



tan °*l{ = - -M- where n « 1, 2, 3, . . . [M! 

 a aMa^j 



and solved graphically for a^. 



CONCLUSIONS 



I 

 A method of computing the dynamic tension at any point 

 along a mooring cable for two sets of boundary conditions has 

 been presented. Although the sag of the cable was neglected in 

 this analysis, it is felt that the real ship-anchor problem will 

 lie between the two sets of boundary conditions. The case with 

 the lower end of the cable rigidly fixed should predict a value 

 for the tension higher than the real case; whereas, the casp with 

 the lower end of the cable free to move should predict a value 

 for the tension lower than the real case. 



20 



