Page 13 - Vibrations 5

2
= or = √

The natural frequencies are = 1 and = √2/5
1
2
You do not need to know about the damping to determine

the natural frequencies within the structure.

1 0 0 ̈ 1 + 2 − 2 0 ̇ 1
1
( 0 2 0 ) (̈ ) + ( − 2 + 3 − 3 ) (̇ )
2
2
2
0 0 3 ̈ 3 0 − 3 + 4 ̇ 3
3
+ 2 − 2 0 1 1
1

+ ( − 2 + 3 − 3 ) ( 2) = ( )
2
2
0 − 3 + 4 3 3
3

As before, when there is no damping, this can be written

as,

̈ + = 0

12