oscillation and the dampingo The resonant frequency was between |jl = 2tt/41 

 and |JL - Zy^lAZ and the ratio of observed damping to critical damping was 0.16. 

 When these calibration values are used, equation (8, 26) can be put in the form 

 given by equation {8, 28)o 



(8«28) -^ +-^-^z + z = aoi{fi)costJLt 



in which \i^ is 2tt/41o The true resonant frequency works out to be 2ir/41,5 

 (a period half way between the two observed values) and the damping is 0. 16 

 of critical damping. 



Ttie motion of the -wave pole under the above conditions is given by 

 equation (8, 29). 



(8„ 29) [1 - (H'/M-o)]aQ0{H.) cosjo-t K(ix/(j.^) a^ (5(|j.) sin (j.t 



[l = (lJL/ii^)2]2+K2{jx/fjL^)2 [l.(^l/HL/]^ + K2(^x/M.o)^ 



in which K equals 0. 32„ 



For |JL corresponding to a period of ten seconds, the coefficient of the 



cosine is positives and the sine term is small compared to the cosine term. 



Therefore the wave pole will move up as the crest of a wave passes and the 



height of the recorded wave will be less than the height of the actual wave. 



The forcing function tends to force the pole downward in a wave crest, but the 



left hand side of the equation is so far past resonance at the high frequency end 



that an additional 180 degree phase shift is introduced, and the wave pole 



naoves up in a passing wave crest. 



The height of the water on the moving wave pole was recorded, and the 



spectrum of this function is to be obtained. What is desired is the spectrum of 



77 



