## An Improved Method for Calculating Free Vibrations in Systems of Several Degrees of Freedom |

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accomplished by matrix amplitude ratios Appendix canonical form coefficients Collar method constants of integration convergence coordinates correct amplitude degrees of freedom Determination of Higher-Frequency displacements and velocities DnOin Duncan and Collar elements Equation 12 expand the determinant find the A's find the motion finding the modes found to three free motions free vibration frequency equation funda fundamental frequency fundamental mode higher mode Higher-Frequency Modes initial amplitudes initial conditions initial displacements latent roots linear equations matrix algebra matrix language Matrix Method matrix of order matrix product matrix theory mental mode mode is lacking Modes of Vibration natural frequencies number obtained one-column matrices original dynamical matrix original system Premultiply pth powers radians per sec relative amplitudes repeated multiplications represent any free row and column satisfy Equation second mode set of amplitudes significant figures similarity transformation single matrix equation solution subtract An/An theorems vibration lacking Xj.p zero