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I have a burning question,

I was trying to find the solutions for a double mass coupled oscillation. So I found out the eigenvectors and then I arrived at this step

[tex] \left( \begin{array}{c} \ddot{x_1} \\ \ddot{x_2} \end{array} \right)=\lambda \left( \begin{array}{c} x_1 \\ \ x_2 \end{array} \right) [/tex]

(the second matrix is without the accents, I think the latex code will take a while to refresh)

ok so my question is, why is one of the solutions displayed as

[tex] x_{1}+x_{2}=A_{1}\cos{(\omega t+\phi)} [/tex]

when from the first equation, it is evident that

[tex] \ddot{x_1}=\lambda{x_1} [/tex]

so

[tex] x_1=A_1\cos{(\omega t+\phi)} [/tex]

I simply don't understand why the above is not acceptable. Also, I am having trouble in relating the addition of the equations (equation 2) to the solution for the eigenvectors. By the way, I also know the solution for the eigenvectors.

I was trying to find the solutions for a double mass coupled oscillation. So I found out the eigenvectors and then I arrived at this step

[tex] \left( \begin{array}{c} \ddot{x_1} \\ \ddot{x_2} \end{array} \right)=\lambda \left( \begin{array}{c} x_1 \\ \ x_2 \end{array} \right) [/tex]

(the second matrix is without the accents, I think the latex code will take a while to refresh)

ok so my question is, why is one of the solutions displayed as

[tex] x_{1}+x_{2}=A_{1}\cos{(\omega t+\phi)} [/tex]

when from the first equation, it is evident that

[tex] \ddot{x_1}=\lambda{x_1} [/tex]

so

[tex] x_1=A_1\cos{(\omega t+\phi)} [/tex]

I simply don't understand why the above is not acceptable. Also, I am having trouble in relating the addition of the equations (equation 2) to the solution for the eigenvectors. By the way, I also know the solution for the eigenvectors.

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