Analysis 



Definitions 



k - linearized nylon rope spring rate (lb/ft) 



m - effective mass of ALVIN (includes added mass effect) (lb - s&c^jh ) 



c - linearized damping due to water drag (lb - sec/ft) 



Y - displacement of MIZAR (feet) 



X - displacement of ALVIN (feet) 



From Figure D-5, 



mx + ex + k(x - y) = (1) 



Let z = X — y , which is the relative motion between MIZAR and ALVIN. Substituting 

 into eq. (1) gives, 



mz + cz + kz = my + cy (2) 



Assuming sinusoidal motion, 



y = Y sinij) t 



where V = amplitude of steady oscillation 



2t 



T = period of ship motion 



A solution to eq. (2) can then be assumed as, 



z = Z sin (u)t — 4> j 



and eq. (2) solves to give 



Ik -mu^ )^ + (cu)^ 



(3) 



Letting 



u 



m 



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