4. For the system shown,
$m_1 = 1 kg$, $m_2 = 4 kg$, $k_1 = 10 N/m$, $k_2 = 2 N/m$, and $k_3 = 10 N/m$
(a)Write the equations of motion in matrix form
(b)Find the eigenvalues and eigenvectors for the system
(c) Draw clearly the mode shapes displaying the relative motion of the masses.
(d) Identify any nodes for the system.