A system of differential equations can be created for two masses connected by springs between one another, and connected to opposing walls. The dependent variables form a 4 × 1 vector y consisting of the displacement and velocity of each of the two masses. For the system y′ = Ay, the matrix A is given by:
0 0 1 0
0 0 0 1
* * * *
35 −5 0 −12 (Note that the third row of A is not given.) Because the system oscillates, there will be complex eigenvalues. Find the eigenvalue associated with the following eigenvector.
−7i
7i
14 + 42i
−14 − 42i