ClearAll["Global`*"];
MinverseK := {{(k1+k2)/m1, -k2/m1}, {-k2/m2, (k2+k3)/m2}};
MatrixForm[MinverseK]

Eigenvalues[MinverseK]

Eigenvectors[MinverseK]

matrix =  MinverseK /. {k1->k, k3->k, k2->k, m1->m, m2->2m};
MatrixForm[matrix]

Eigenvalues[matrix]

Eigenvectors[matrix]

N[%]

N[Eigenvalues[matrix]]

%[[1]]/%[[2]]

x1[t_] := (A/2) (Cos[ω1 t] + Cos[ω2 t]);
x2[t_] := (A/2) (Cos[ω1 t] - Cos[ω2 t]);
ω1 = 1.0 ; ω2 = 1.1; A = 1;
Plot[{x1[t], x2[t]}, {t, 0, 100}]