214 SYMPOSIUM ON AERONAUTICS. 



For p==o, the second is about half the first; for /?= co, the two 

 are equal ; the numerators therefore do not differ greatly in magni- 

 tude for any value of p: 



The ratio of the denominators is 



r (.03924 -^^-)-+-i308y ]'^^ 

 L (23-37 - P'T- + S.2>29'P' J ' 



and is very small when p is less than i. For larger values of p, we 



have approximately 



i/R^~=^i-i-2S.2/p^- + S45/P*- 



Hence the short oscillations may be neglected when /» < i without 

 introducing much error; but as p increases beyond the value i, the 

 importance of the short oscillation grows rapidly. 



6. Consider first the case p < i, neglecting the short oscillation. 

 The particular solutions for u, zv, and 9, that is, lu, Iw, Iq, are ob- 

 tained from the imaginary parts of 



u — .01601 ^i + .04263 , „. „ „ . 



- = , n , - (.i28pH -f i.iGp- - 3.385^^ 



J -p'' + .i308pt + . 03924^ ^ ^ ^ ^^^^ 



— .917) e'P^, 



w — .oi6oi^i + .04263 , ,. , ^ „x . . (a') 



J = _ p. ^Jspi+ 0392 -4 ^■'''^'' + "458^^).-, (4) 



J - ^2 -f .1308/)/ + .03924 



To estimate the value of p corresponding to the maximum dis- 

 turbance we may examine the amplitude of 6/ J, which is 



'd ^ V (. 04263) ^ + ( .016 jp)^ -\'-' 



The calculation gives /^-^ 0.0394 or /) = 0.1985. The value of the 

 amplitude is then about 0.0095/ radians or 0.54/ degrees. If / 

 should be 20 ft./sec, the forced oscillation would have an ampHtude 

 of about 10°. 



7. As the use of /?=; 0.1985 in calculating is somewhat more 

 complicated than the use of p = o.2, and as the change from 0.1985 

 to 0.2 does not materially alter the amplitude of the forced oscilla- 

 tion (and probably does not exceed the error of observations), we 



