Assume 



Substituting into eq. (8), 



F^ = 282 (x)^ 



Using Taylor series linearization, 



Fq « 564 |x^| X (9) 



where xq = average velocity 



Therefore, the damping coefficient, C , can be expressed as, 



C ^ 564 \xq\ (10) 



Since the winch haul-in velocity is 35 ft./min., x is assumed to be, 



35 

 xr, = — = -584 ft. /sec. 

 ^ 60 



:.C = 564 (.584) = 3291b. - sec. /ft 



r= -£— =-I^M. (11) 



Determination of Linearized Spring Constants 



Four different nylon ropes are considered in this report. These are: 



4V2-inch circumference Plimoor nylon rope 

 8-inch circumference Plimoor nylon rope 



67 



