Question $3-$ Finding the eigenvalues $($frequencies$)$ and eigenvectors $($mod shapes$)$ of a $2$DOF mass$-$spring system

Please notice that Figure $4$ depicts a simple mass$-$spring system. Form the mass & stiffness matrices and calculate the structural periods as well as the mode shape vector!

$\backslash$table$[[$Table $1.$ Parameters$],[$Variable$,$Value$],[m_1,2\mathrm{.}0$ kg$],[m_2,1\mathrm{.}0$ kg$],[k_1,1000\frac{N}{m}$