Loaded Shaft supported in Three Bearings. 653 



+ -796r 2 4--1749r 3 , 



fu 5 = 635^! + l-583w 2 + l-646w 3 + i"178w 4 4- *375ie 5 + -1102^ 



+ B 396f7a + -0887v 8 , 



\jr-c! = -444wi + -77i« 2 + '65h 3 + '4705^ + '1304 u 6 + '46^ 



+ l-763r 2 + -412»„ 



^ri« 2 = -426^ + ' 748« 3 + -6295w 3 + '455w 4 + '1265u 5 + •532» 1 



+ 2*342 v 2 +'6145v 3 , 



fv 3 = -301 Wl + -535^ + -445^3 + *318w 4 + -08845*5 + '^l^ 



+ 2*055r 2 + -626r 3 . 



Hence, eliminating the displacements, 



1-784- 



■rp 3-4 



2945 



2-15 



•57 



•376 



1-232 



•2635 



1-995 



4-6-4/ 4-28 



324 



•821 



•3845 



1-27 



•2745 



1-749 



4-285 



4-305- 



4 3-28 



•806 



•327 



1-084 



•2345 



1-29 



3-275 



3-432 



2-66-^ 



•587 



•24 



•796 



•1749 



•635 



1-583 



1646 



1-178 



•375-4/ 



•1102 



•396 



•0887 



•444 



•77 



•65 



•4705 



•1304 



•46-4/ 



1-763 



•412 



•426 



•748 



•6295 



•455 



•1265 



•532 



2-342- 



-4/ -6145 



•301 



•535 



•445 



•318 



•08845 



•421 



2-055 



•626-4/ 



The solution of this deter minantal equation in -ty gives 

 the various whirling speeds. We determine the two largest 

 roots approximately by substituting trial values of yjr, and 

 seeing i£ the determinant is positive or negative. 



Tn this way we find 



Yalue of 4 / . 



Approximate value of determinant 



'CO 





4- co 



15 





4-2-18xl0 8 



14 





+ 5-55 xlO 7 



13 





-1/23 xlO 7 



2-5 





-l-82xl0 2 



2 





+ 2'18xl0 2 



— 00 





+ QO 



Hence there is a root between 13 and 14, and one between 

 2 and 2*5. Closer examination of these regions will lead to 

 a closer value of the root. The sum of the eight roots, being 



