Question

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

Answer 1

let the third row of the matrix is a,b,c,d

.

and eigenvector is

if v is an eigenvector of the matrix A then

compare the first entry

.....................eigenvalue

.