Consider the mass-spring system in Figure. The frequencies for the mass vibrations can be determined by solving for the eigenvalues and by applying Mx + kx = 0, which yields

Applying the guess x = x₀e^iωl as a solution, we get the following matrix:

Use MATLAB’s eig command to solve for the eigenvalues of the k – mω² matrix above. Then use these eigenvalues to solve for the frequencies (ω). Let m₁ = m₂ m₃ = 1 kg, and k = 2 N/m.

-k -k --k 2k --k -k 2k IN3