2014/5/12 REVIEW:Free vibration of SDOF Free vibration of undamped SDOF u(t)=e" mii+cu+ku=0 心A = ⊕ u(0）=4cos is sino! Free vibration of underdamped SDOF Other scenario ·Critically damped Viscously dampingem 0=[u(0)1+o)）+i(0)r]e✉ u()-[u(0)+(u(0)+i()):e ·Overdamped u0=ew(4em+4em） Coulomb damping syste %=a尽490 Other scenario Undamped SDOF mii+ku=po sinot Negative-damped system Complementary Solution u() u)-cov4sinh(o)cosh(o mii+ku=0 u.(1)=Acos@t+Bsin@t Particular solution:response due to Psin up(t)=Csinot+Dcosot 22014/5/12 2 REVIEW: Free vibration of SDOF mu cu ku    0 ( ) st u t e  n k m   2 2 c c m km       0 0 0 cos sin n t n D D D u u u t e u t t                          0 0 cos sin n n n u u t u t t            2 1    D n   Free vibration of undamped SDOF Free vibration of underdamped SDOF Viscously damping system Coulomb damping system Other scenario • Critically damped • Overdamped   0 1 0     n t n u t u t u t e             0 0 0       n t n u t u u u t e               ' ' 1 2 n D D t t t u t e Ae A e                  2 1 ' 2 2 ' 0 1 0 2 0 1 0 2 n D n D u u A u u A                   ' 2 1    D n   Other scenario • Negative-damped system       2 2 1 2 sinh 1 cosh 1 n t n n u t e A t A t                 Undamped SDOF 0 mu ku p t   sin • Complementary Solution • Particular solution: response due to u t c   mu ku   0   cos sin c n n u t A t B t     0 p t sin ( ) sin cos p u t C t D t    