MT-1620 al.2002 The determinant 0 (225) There will be n eigenvalues for an n degree-of-freedom system In this case eigenvalue natural frequency n degree-of-freedom system has n natural frequencies Corresponding to each eigenvalue(natural frequency), there is an Eigenvector-- Natural Mode Place natural frequency o into equation(22-4) Since determinant =0, there is one dependent equation, so one cannot solve explicitly for A. However, one can solve for the relative values of the components of A in terms of (normalized by) one component Paul A Lagace @2001 Unit 22-4MIT - 16.20 Fall, 2002 The determinant: k − ω2 m = 0 (22-5) ~ ~ There will be n eigenvalues for an n degree-of-freedom system. In this case: eigenvalue = natural frequency ⇒ n degree-of-freedom system has n natural frequencies Corresponding to each eigenvalue (natural frequency), there is an… Eigenvector -- Natural Mode • Place natural frequency ωr into equation (22-4): [ k − ωr 2 m ] A = ~0 ~ ~ ~ • Since determinant = 0, there is one dependent equation, so one cannot solve explicitly for A. However, one can solve for the ~ relative values of the components of A in terms of (normalized ~ by) one component Paul A. Lagace © 2001 Unit 22 - 4