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i.e. is not invertible. It follows that the determinant of the matrix must be equal to 0, so:

Solving for , the two positive solutions are:

Substituting into the matrix and solving for , yields . Substituting results in . (These vectors are eigenvectors, and the frequencies are eigenvalues.)

The first normal mode is:

Which corresponds to both masses moving in the same direction at the same time. This

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