Homework 23 Solution

Homework 23 Solution - Lecture 23 MEEN 357 Homework...

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Lecture 23 MEEN 357 Homework Solution 1 Lecture-23-Homework-Solution.doc RMB 1 u 1 m 1 k 2 m 2 k 2 u 3 k 3 u 3 m 5 k 4 m 4 k 4 u 1. Consider the four degree of freedom vibrating system shown in the following figure. The equations of motion of this system are ( ) ( ) ( ) ( ) ( ) ( ) ( ) 2 1 1 1 1 2 2 1 2 2 2 2 2 2 1 3 3 2 2 2 3 3 3 3 2 4 4 3 2 2 4 4 4 4 3 5 4 2 d u m k u k u u dt d u m k u u k u u dt d u m k u u k u u dt d u m k u u k u dt = − + = − + = − + = − (23.1) a. Derive the normal form of the system (23.1). Solution Define
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