3. Rewrite the second-order differential equation for the mass-spring system as a linear system…

3.          Rewrite the second-order differential equation for the mass-spring system as a linear system and find the eigenvalues. Do you see any connection with our earlier method of solving this system?

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4.           a.    What are the eigenvalues and eigenvectors of the matrix

 

a     b 1

            )

 

1 –b    a   ?

b. Determine the types of the equilibrium points for the linear system corresponding to the above matrix, and sketch the regions in the   ab plane where this matrix has different types of eigenvalues.