The meaning of eignvalues in vibration

[Zouatine]

Homework Statement

vibration of frame

Relevant Equations

m*a+k*x+c*v=q

when i solved simple example about 2 height stories when we have 2 degree of freedom I’m confusing about the meaning of result of eigenvectors and eigenvalues .
This is the example

i'm getting 4 eigenvalues and 4 eigen vectors . as following

I didn’t understand we have 2 MDOF and we are getting 4 values of eigenvalues and also eigenvector each vectors has 4 component , the eigenvector means the displacement of MDOF .

thank you

 

[FactChecker]

When you count all the state variables, position, velocity, acceleration, etc., that your model includes, how many degrees of freedom are there? Don't forget that in the general situation, you might start with nonzero initial conditions for positions, velocities, accelerations, etc.