University of Florida/Eml4507/s13.team3.GuzyR5

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Problem 5.1

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

Given[edit]

Find[edit]

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[edit]

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: