Noneinusoidal Osoiltations of a Cylinder in a Fvee Surface 



-155 

 -150 

 (f 1-145 

 -140 

 -135 



25 



20 



15 



10 



1.0 



1.2 



1.4 



1.6 



1.8 



2.0 



Fig. 10 Phase angles of first- and second-order waves 



at |x| = oo vs. X. for \| = 10b 



We then define 



^^6.= ^ 



and 



^6b b^ • 



In Fig. 10 the phase angles qg (see Eq. (76)), 9g' , and qj - q, 

 are shown as functions of \ for \i = 10b. 



VII. DISCUSSION 



If the forcing motion on a floating body has a very narrow 

 frequency band,most of the second-order hydrodynamlc responses 

 occur in a frequency range of about twice the forcing frequencies. 

 However, two components of the second-order force are exceptions 

 to this case. One Is the steady-state force and the other Is the' 

 force with frequency equal to the difference-frequency between a 

 pair of the frequencies In the narrow-band spectrum. If the value 

 of the difference-frequency, o-, - ^2.' ^^ very small, the force which 



937 



