N on sinusoidal Oscillations of a Cylinder in a Free Surface 



1.0 



0.8 



«- 0.6 



0.4 



0.2 



1.0 1.2 1.4 1.6 1.8 2.0 X 



Fig. 7 First- and second-order forces vs. X. for \^ = 20b 



^2= g (<^l - ^2^ 

 .2 



j: 



h (e) cos K e de , 



o 6 I 



Yeb = 772 ^'Q2'^i^2<K 1-^2) 



Furthermore we can reduce the above expression to 

 .j{cr, -o-g)! 



Ye{x)e 



where 



6a 



cosJK lx| - (a -crjt+e -j 



- Yg^cos j(K, - K2)|x| - ((T, - a^)t - (q, - q^ \ 



1/2 



Y6a= [^1+^2' +2A,A2Cos (q^ + 6^)] . 



e^' = tan" 



A2 sin 6g - A| sin qg 

 Ag cos 9g + A| cos qg 



935 



