AND VIBRATION OF SHAFTS. 
355 
Case of tivo or more Pulleys. 
59. So far (Cases IX.-XVI., §§ 23-58) we have only fully investigated the effect 
of one pulley on a shaft supported in different ways, the effect of the shaft being 
neglected. It was shown in §§ 19, 20 that, even in simple cases, the equations 
obtained by considering the shaft and a single pulley together were too complicated 
to allow of a solution in a form convenient for practical application. The following 
case will show that, even in the simple case of a shaft freely supported at the two 
ends, the equations obtained by considering the effect of the two pulleys together— 
the effect of the shaft being altogether neglected—are also too complicated to allow 
of a solution which can be readily applied to any actual case. 
Case XVII. 
60. Shaft, length I, merely resting on a support at each end and loaded 
WITH TWO PULLEYS, WEIGHTS Wg, AND MOMENTS OF INERTIA T^, L, PLACED AT 
DISTANCES Cy, g{ AND C 3 , C 3 ' RESPECTIVELY, FROM THE BEARINGS. 
Thus— 
Fi>. 2.5. 
I-S- 
k - C, - 
Us- 
1 ■ 
1 
M 
“T 
- - -1 - 
—-— 
-<5- 
c 
— >] 
-— ^ 
j 
i 
1 ^ 
I 
L 
w 
t 
1 
Taking the origin at the bearing A, we have (§21, equation 2) 
y = + Cx + D , from A to C, 
y — ^ P" -\- C'x + D', from C to D , 
y" ^ P' -V C'x -f- D", from D to B. 
When 
X = Q , y = 0 , cVyjdx^ = 0 ; 
whence 
D = 0 
( 1 ). 
