Brard 



15.2. "True" and "Apparent" Coefficients 



Now, let us consider the expressions of the forces in harmonic forced 



motions. 



We define the "apparent" coefficients of the motion by the following 

 formulae: 



a) From par. 14, Eq. (11), we deduce: 



'6jL 



2W 2W , ^ \U, 



AL ^^+ ^3,pp) = AL ^^+ ^3) + 3 ^J[J^ (without planes), 



IcoL] /wL\ 



^^ + ^3,pp^ = AL Ca^+A^3) + ^ HJIJ- + ^ T'^L/iB cJL/V (with planes), 



AL 



y (2) 



1-0(0)- f 



coh 



(without planes), 



1-0(0)- f('^ 



+ 2 



1 _ f l^ 



(with planes) . 



b) The first equation of Eq. (13), par. 14, gives: 



2W - 2W , _ ^^ I U 



AL ^13 ^pp - AL ^13 ^ ^L/U 



c) From par. 14, Eq. (15), it follows: 



(3) 



2W 

 AL 



2W 

 AL 



(i'35 +M<fG) = AL (^^^35 +^^G^ + ^' g' (~^)/i^) (without planes). 



mf 



AL ^^35 3pp+^^5) =AL ^"35+A^^g)+« g i-uJ/l-U 



+ ^T (^B^Lj^-^^mJ ^iBgiB (^)/(t) (*^t^^ planes) , 



M4) 



2W , 



If (M3-M1) + aa 



2W 



AL 



2W , 



^ (M3-M1) + a^ 



(Ma - Ml) + a' 

 app - AL CM3-Mi) + a' 



PP AL 



2W 



1-0'(O)- f 

 1 - 0'( ) - f 



, jcoL 



U 



"u 



(without planes) , 



A \^B_ Lg mg^ 



1 , e /^L 



l + ^lBflBilf 



(with planes) 



890 



