Vibrations of a Hod of Varying Cross -Section, 

 By interpolation the node is found to be at the point 



x = 3-64662, z/l = -239799. 

 The point of maximum excursion is given by 



91 



dx 



/C= -215563^-354-429 

 / ax 



dx 



= 0. 



We may notice that 



2*= *, = ;!#•.) and ^^-^^-ij/av) 



I find as corresponding values : 



2 V*. 



x. 



jh 9 



dx' 



dx ' 



&a 



j 5-16 

 1 5-18 



6-6564 

 6-7081 



3-08065 

 3-11787 



•00124091 

 •00223670 



+ -224260 

 -•120653 



Hence the point of maximum excursion is found to be at 



x = 6-69001, z/l = -439930. 

 At the point of inflexion 



We note that 



d 2 <j> _ d<f> l _ 1 _ , 



^ _ aZ — 92 — ^3~2 ^ w v#), 



and 



'215563 ^o_ 354 . 429 ^o = Q> 



ar 



d^h__djri _ _JL 



^ 



efo? 



= ^2=-37 2 J 3 (2 V / ^)- 



ar 



The following are corresponding values : 



2 Va:. 



#. 





S/ a 



(-6-28 



16*30 



• 



9-8596 

 9-9225 



1-305855 -000971393 

 1-320731 000769200 



-•062796 

 + -012074 



