Q5.7   M-K system  p.100

mm = DiagonalMatrix[{20, 6, 9}]
kk = {{80, -60, 0}, {-60, 78, -18}, {0, -18, 
            36}};
MatrixForm[kk]

aa5 = Inverse[mm] . kk; MatrixForm[aa5]

{λ, ϕt} = Eigensystem[aa5];
λ
ϕ = Transpose[ϕt]; MatrixForm[ϕ]

ms = Simplify[ϕt . mm . ϕ]
ks = Simplify[ϕt . kk . ϕ]

Table[ks[[i, i]]/ms[[i, i]], {i, 3}]