Page 546 - Thomson, William Tyrrell-Theory of Vibration with Applications-Taylor _ Francis (2010)

Answers to Selected Problems 533

m j
nil
8-9 -A

{k, + k. + k,) -^2 -^5 0
~^2 (^2 + ^3) —/C3 0 = 0

~k, -^3 (A3 + A4 + A5) - k
0 0 -A 4 A4
1
’ 100 0 1 0
0 1600 1 1
8-12 -A
4.969 0
0
1 0 4.969
1
5000 3500 1 - 2400 -2 6 0 0 ]
3500 127,250 1 10,800 -14,300
- 0
- 2400 10,800 1 40,800 0
-2600 14,300 1 0 41,000 J
Solution by CHOLJAC with \ = co^
A, == 50.37 A2 - 78.77 A3 = 8208 A4 = 8256
0), = 7.097 0)2 = 8.87 0)3 = 90.59 a>4 = 90.86
/. = 1.130 cps f2= 1-413 /3 = 14.43 h = 14.47

EL 1.00 \
8-13 = 0 .2 2 3 ^ ^ , </> - I 2 58s}’ = 0.47741
,
p ’ "2 W 1.932/
8-14 io, = 0.584 ^2 = 1.2001/ — , 0^3 = 1.642W —

8-15 w, = 0.29251 0)2 = 1.916W— ^ , 0)3 = 5.146i
mP ’
1.0000 \ 1.0000 I 1.0000
0.5318 , <^2 1 - 1.507 -3.2481
0.1565 1 - 1.2687 i 4.6471

8-18 U'U = K, K, U = - 1.414 -0.707'
0 1.875
1.667 -0.5774

8-20 A/ = 0, A =
-0.5774 2.0

8-22 A = o), = 0.769 o). = 1.187
k ’
. /0.816\ -0.816\
= \1.00 / ’ ^2 - 1.00 /