- #1
cue928
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I am doing a spring mass problem. Unfortunately, I'm not proficient in Tex so this won't be as neat as it could be.
Data: m1=1, m2=1; k1=0, k2=2, k3=0
Stiffness matrix:
-(k1+k2) k2
k2 -(k2+k3)
1 0 * x1'' -2 2 * x1
0 1 x2'' = 2 -2 x2
From that, I get the following equations:
x1'' = -2x1 + 2x1
x2'' = 2x2 - 2x2
I then generate the following matrix:
[tex]
\begin{bmatrix} -2-\lambda & 2\\2 & -2-\lambda\end{bmatrix}
[/tex]
Using x for lambda:
(-2-x)^2 - 4
x^2 + 4x = 0
I get r = +/- 2i, but according to the book I should get frequencies of 0 and 2 [ (omega)^2 = -lamdbda)
Where did I go wrong? I verified that I wrote it down correctly from the book but I still don't see it. All other problems on this section make sense.
Data: m1=1, m2=1; k1=0, k2=2, k3=0
Stiffness matrix:
-(k1+k2) k2
k2 -(k2+k3)
1 0 * x1'' -2 2 * x1
0 1 x2'' = 2 -2 x2
From that, I get the following equations:
x1'' = -2x1 + 2x1
x2'' = 2x2 - 2x2
I then generate the following matrix:
[tex]
\begin{bmatrix} -2-\lambda & 2\\2 & -2-\lambda\end{bmatrix}
[/tex]
Using x for lambda:
(-2-x)^2 - 4
x^2 + 4x = 0
I get r = +/- 2i, but according to the book I should get frequencies of 0 and 2 [ (omega)^2 = -lamdbda)
Where did I go wrong? I verified that I wrote it down correctly from the book but I still don't see it. All other problems on this section make sense.