rat. 1 COs--sin cos(o+) coS(@-)t-( 2 Tat. 1 + cOS sin( o )} Al rat { sin ot na sIn ot]+sin )} 0 0+ u( 1) a 7 op-r a losin u sin ot 由外力决定的 n(x,1)=∑(A1cos +B1Sm灯mt naat n7 由初始条件决定的 初值确定叠加系数:A nTs nIs P(ssin-ds: B y(ssin ds n u(x, t=u(x, t)+u(, t)sin( ) } 1 sin( ) 1 cos [ )] 1 1 cos( ) ( 1 cos( ) 1 cos { sin [ 2 t l a l a t l a l l a at l a l a t l a l a t l a l l a at l x a Al                         − − + − + + − + + − − − + + + = − )} 1 1 sin ] sin ( 1 sin 1 cos {[ 2 l a l l a at t l a t l l a x a Al              − + + + − − + = ( , ) cos { sin sin } 2 2 2 2 2 t l a l at l a l l x a Al u x t II         − − = ( , ) ( cos sin )sin . 1 l n x l n at B l n at u x t An n n I    =  +  = 初值确定叠加系数： ( )sin ; 2 0      d l n l A l n  = ( )sin . 2 0       d l n n a B l n  = u(x,t) u (x,t) u (x,t) I II = + 由初始条件决定的 由外力决定的