<$»£)0-w&i-)--i-( S KS&)-'> 



and solving for oo 2 a 2 yields the resonant frequency of the new model: 



3Po a c a 2 A 2s \ 



o) 2 a 2 = B2i J 3p 0a c a 2 a / 



/ 11E 2 \ 



( 1+ 3^c7aT-) (»'-23) 



Now [42], 



Po a Ca 2 = YaPoa (III-24) 



and from equation 11-1 15, 



P - P + 2s - p 4. 2s 



^o a - r 0( +— - P 0w +— . (III-25) 



Therefore, substitution of equations III-24 and III-25 into III-23 yields: 



3v a P 2s 



" +_£i(3 Ya - 1) 



u) 2 a 2 = -22 E°£ (in-26) 



11E 2 



Pot P 0( a 



\ 3p 2 c f 2 a 2 ) 



The damping factor, H, will be defined by 



CDo _ Pow^ 3 . 2E 





+ 



Po, c w Po,wa 2 



3(Y a - 1) / <0K a V /2 /, 



/ <DK a \™ / ^S \ 



coa (2^) V + T^*)- C»-27) 



Thus, following Devin [19], 



+ r]-+4=d, (IH-28) 



H rari hL, H 



rad ' 'vis ' 'th 



where 



Mrad ~ 0) 2 p 0w a ' (MI-29) 



u = tQoPo,a 2 



2^ ' (Hl-30) 



and 



H,h " 3( Ya - 1) V o)K a >/ V 1 + p ,ca 2 a3 ^ C 11 " 31 ) 



As before, at co = co , H = Q. Thus, substitution of equations III-26 and III-27 into 111-19 yields: 



21 



