2014/5/12 .From the above equation ·Complete solution --sp- u(t)=u+u u()=(Acos+Bsin)+(Csint+Dcosor) c--o1f月-ola Complete solution of undamped system u(t)=Acos+Bsin+(Csinot+Dcosor) x-oiaj-[la ·Total response ·Resonance C-(ola( p="-bl于(ele) C=0D=- ·Total response 0=(cm+Bsno小-2osm ·Initial conditions .Consider transient response or not? B-2 .Numerical calculation methods Expression of total response in resonance .Variation of response amplitude at resonance 2014/5/12 5 • From the above equation 2 1 2 st n n C D u                             2 2 1 0 n n C D                                   2 2 2 2 1 / 1 / 2 / n st n n C u                        2 2 2 2 / 1 / 2 / n st n n D u                    • Complete solution • Complete solution of undamped system   c p u t u u      cos sin   sin cos  n t D D u t C e A t B t t D t           u t C     A t cos  D D  Bsin t  sin  t t  Dcos  • Total response • Consider transient response or not? • Numerical calculation methods • Resonance • Total response • Initial conditions       2 2 2 2 1 / 1 / 2 / n st n n C u                        2 2 2 2 / 1 / 2 / n st n n D u                    C  0 2 st u D       cos sin cos  2 n t st D D u u t e A t B t t          2 st u A   2 2 1 st u B    • Expression of total response in resonance   2 cos sin cos 2 1 n st t D D n u u t e t t t                             • Variation of response amplitude at resonance