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Two blocks oscillating via springs is a 2 DOF system. The final solution will have the form of a

a modal vector times cos(w1t - phi1) + another modal vector times cos(w2t -phi2).

The system is hence said to be oscillating at two natural frequencies w1 and w2.

The modal vector for an n DOF system is {A1, A2, A3...An). Note that we can't find the exact vector because we are short one piece of information, hence we need initial conditions.

The natural frequencies and mode shapes can also be found by analyzing eigenvectors (=modal vectors) and eigenvalues (natural frequencies ^2).