University of Florida/Eml4507/s13.team3.ADR6

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

Given
$$ m_{1}=3 $$

$$ m_{2}=2 $$

$$ k_{1}=10 $$

$$ k_{2}=20 $$

$$ k_{3}=15 $$

Find
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
First plug given values into the stiffness matrix:

$$ K= \begin{bmatrix} a_{1}&0&0&-a_{1}&0&0\\ 0&12a_{2}&6La_{2}&0&-12a_{2}&6La_{2}\\ 0&6La_{2}&4L^2_{2}&0&-6a_{2}&2La^2_{2}\\ -a_{1}&0&0&a_{1}&0&0\\ 0&-12a_{2}&-6La_{2}&0&12a_{2}&-6a_{2}\\ 0&6La_{2}&4L^2_{2}&0&-6a_{2}&4La^2_{2}\\

\end{bmatrix}$$

$$ K= \begin{bmatrix} (10+20) & -20\\ -20 & (20+15)\\ \end{bmatrix}$$