For the system shown,

$m_1=1kg,m_2=4kg,k_1=10\frac{N}{m},k_2=2\frac{N}{m},$ and $k_3=10$N$/$m

$($b$)$ Find the equations of motion in matrix form

$($c$)$Draw cleagenvalues and eigenvectors for the system of the masses the mode shapes displaying the relative motion

$($d$)$Identify any nodes for the system.