ABSTRACT
In the basic method, the eigenvalues of the system are found from the roots of the polynomial equation obtained from the characteristic determinant. Each of the roots was then substituted, one at a time, into the equations of motion to determine the mode shape of the system. Although this method is applicable to any N-DOF system, for systems with DOF greater than 2, the characteristic equation results in an algebraic equation of degree 3 or higher and the digital computer is essential for the numerical work. As an alternative to this procedure, there is an implicit method of transformation of coordinates coupled with an iteration procedure that results in all the eigenvalues and eigenvectors simultaneously. The Gauss method offers one way in which to solve for the ratio of amplitudes. Essentially, the Gauss procedure reduces the matrix equation to an upper triangular form that can be solved for the amplitudes starting from the bottom of the matrix equation.
