system eigenvector

$U=\left[\begin{array}{ccc}-0\mathrm{.}16& 0\mathrm{.}47& 0\mathrm{.}05\\ -0\mathrm{.}33& -0\mathrm{.}08& -0\mathrm{.}28\\ -0\mathrm{.}41& -0\mathrm{.}19& 0\mathrm{.}53\end{array}\right]$

system values

$k_2=800\frac{N}{m},k_1=900\frac{N}{m}$

$k_3=600\frac{N}{m}{k}_4=950\frac{N}{m}$

$k_5=750\frac{N}{m},k_6=500\frac{N}{m}$

$m_1=5kg,m_2=4kg,m_3=2kg$

a$)$ Obtain the inertia matrix and stiffness matrix of the system

b$)$ Determine the natural frequencies of the system using the rayleigh method

c$)$ Obtain the equations of motion of the system $(x1(t),x2(t),x3(t))$