<p>The response to excitation in the axially loaded Timoshenko rod is greatly influenced by the type of axial load, which could be compressive or tensile. The results presented in this article have practical applications, particularly when the axial load is compressive, as non-positive eigenvalues indicate possible buckling. The mathematical model leads to an eigenvalue problem. Abstract theory from a recent article is presented and applied, demonstrating that partial sums of modal solutions converge to a solution of the model problem. This enables one to predict the response of a given structure to excitation.</p>