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0.0S 





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0.6 0.7 0.8 0.9 1.0 



RELATIVE FREQUENCY, U/Up 



Figure 7 — Neumann Spectrum Normalized with Respect to Frequency 

 and Amplitude of Peak 



is a function only of w/cj since knowledge of an approximate polynomial expression for a 

 certain peak frequency spectrum automatically yields an approximation for all peak frequencies 

 by making a suitable linear scale change in s. 



By trial and error techniques common to the electrical engineer, a polynomial approxi- 

 mation was synthesized for approximating the square root of the normalized Neumann spectrum: 



4.85 ^ (S^ + 0.0625 'S + 0.199) (S + 1.385) 

 (S + 0.533)^2 (S^ + 0.536S + 0.199) (S + 1.124) 



The frequency response (at s = jco) of this approximation is compared with the theoretical 

 expression in Figure 8 and is seen to agree quite closely except at extremely low frequencies. 



SYNTHESIS OF INVERSE WAVEMAKER CHARACTERISTICS 



The inverse of the wavemaker frequency response (relating the wave height in the 

 basin to a sinusoidal voltage applied to the wavemaking system) was approximated, again by 

 trial and error methods, by a polynomial expression: 



(S + 1.325)2 (5^ + 0.9S + 3.24) (S^ + 0.295S + 8.71) (S^ + 0.28S + 19.8) 

 {S + 0.3)2 (S2 + 1.44S + 3.24) (S^ + 0.502S + 8.71) (S^ + 0.445S + 1.98) 



(S^ + 2.8TS + 33.1) (S2 + 1.74S + 8.41) 



(S^ + 4.145; + 33.1) (S + 20)' (S + 50) 



10 



