214 



SCIENCE PROGRESS 



- -[T I ?>?'"' '""<*• f + "%> + W) I V"°*' W s . + *y + 



;)p s e-v cos(p » Sit + sv ] 



A(S) s 



- -Clf ? I v" Vcos(i v + ^> + w^V^W,. + e v + 



^p S0 e-°'V cos(pV+£ . 3i )] 



where 



A(8) 



™ + x t 

 g 



N. 



X, 



y„ + 



N, 



g 



w 



X r - -ycos0 o 

 Wsinfl WU 



g 



N r + 



g 



and UtCS), U 2 (8), U 3 (S) ; V.(8), V 2 (S), V 3 (S) ; and R^S), R 2 (8) and 

 R 3 (6") are the cofactors of the constituents of the first column, 

 second column, and third column respectively. 



Let 



U,(8) 



F,(«) 



and consider the solution of 



A(d) 



-n<,t 



F(8)X S e ' cos(p s t + £ s ) 



as a type. We have 

 Let 



F(S) . Pe mt = F(m) . Pe mt . 

 m s = - n s + ip s and P s = Q s 4- iR s 5 



-n B t 



ms, 1 



and X s e ' cos(p s t + S s ) = real part of P s e ' 



e S| (Q s cos p 3 1 - R s sin p s t) ; 



whence we have 



i i 



Qs. = X s cosS: s.> R s. = X s sin£ s 



i£ 5 



X s (cos£ s + i sin£ s ) = X s e '. 



Similarly under the same conditions of solution 



P' = Y c e S2 andP" = N,e 



.-. u = - real part of [~2F (fi)P s eV + 2F S (8)P' S 



nv_ t n" t-i 



^3(8)P" S3 e S 'J 



e s '-' + 2F 3 



s. 



+ free vibrations 



Ui(m, ) 



= - the real part of [s 1 !V P s e m « ( l 



A(m s ) 



t , ,. U,(m' s ) TJ , m' a ,t 



s„ 



3 A(m' ) 



+ fjW*2v» s e m 'V] 



