University of Florida/Eml4507/s13.team3.GuzyR5

Problem 5.1

On my honor, I have neither given nor received unauthorized aid in doing this assignment. 

Given

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Find

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Solve by hand the gen. eigenvalue problem for the spring-mass-damper system on p.53-13, using the data for the masses in (2) p.53-13b, and the data for the stiffness coefficients in (4) p.53-13b.

Solution

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First plug given values into the stiffness matrix:

 


 


 


Next plug stiffness matrix in equation below:

 


Take the determinant:

 


Simplifying:

 

 


Using the Quadratic formula to solve:

 

 

Final gamma values:

 

 


To find the eigenvectors, first we:

 


To solve, lets set   equal to 1:

 


 


 


 


Multiplying out the matrices, we obtain:

 

 


Using the same process we find  :

 


 


Multiplying out the matrices, we obtain: