I solve a mechanical exercise but i had a problem.

I know **M** (mass) and **K** (stifness) matrices (4x4).

I want to solve the (λ^{2}**M**+**K**)v=0 eigenvalue problem, where λ are the eigenvalues and v eigenvectors.

How can i solve this problem. I tried with the Eigenvectors() command but it didn't give the right solution.

The Eigenvalues are okay, but the eigenvectors not

K := Matrix([[4*10^7,-1.50*10^7,2*10^7,0],[-1.50*10^7,1.50*10^7,0,1.50*10^7],[2*10^7,0,8*10^7,2*10^7],[0,1.50*10^7,2*10^7,4*10^7]]);

M:=Matrix([[121.90,99.048,-91.429,0],[99.048,594.29,0,-99.048],[-91.429,0,243.81,-91.429],[0,-99.048,-91.429,121.90]]);

w1,w2:=Eigenvectors(K,M);

Acoording with the book the right eigenvectors(shape mode) are:

[0.013 991, 0.034 233, 0.073 683, 0.090 573]

[0.035 637, 0, -0.032 213, 0]

[0 ,-0.034 233, 0, 0.090 573]

[-0.013 991, 0.034 233, -0.073 683, 0.090 573]

Thank you