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SecondOrder Ordinary Differential
Free Vibrations of Undamped
36 other sections not shown
amplifier amplitude amplitude ratios analog computer angular applied beam calculated circuit circular frequency coefficients complete solution component coordinates corresponding damped spring-mass system damped system damping constant damping factor degrees of freedom denoted differential equation discussed disk displacement eigenvalues eigenvectors elastic elements energy equations of motion equilibrium position equivalent Example external forces Figure forced response forcing function Fourier free-body diagram frequency equation frequency ratio fundamental frequency given by Eq gives harmonic force inertia integration Laplace transform lb/in linear magnitude mathematical maximum method modal matrix mode shape natural frequencies Newton's second law obtain operational amplifier original unbalance particular solution phase angle phase mark plane principal modes principal-mode problem r/min roots rotation shaft shown in Fig small oscillations solving spring constant spring-mass system steady-state amplitude subroutine Substituting system of Fig system shown torsional trial weight undamped values vector velocity viscous damping written zero