MT-1620 al.2002 Boundary conditions. @X=0W=0 @x=e M=EI n=0 With w(x)=C sinh/x C, cosh/x+ C]sin/x+ C4 cos/x Put the resulting four equations in matrix form 0)=0 d 0 dx ()=0 sinh] cosh sin2 coS2 C30 sinh] cosh]I -sin/I -COS2/ IC4 0 Solution of determinant matrix generally yields values of n which then yield frequencies and associated modes(as was done for multiple mass systems in a somewhat similar fashion) Paul A Lagace @2001 Unit 23-8MIT - 16.20 Fall, 2002 Boundary conditions: @ x = 0 w = 0 2 @ x = l M = EI dw = 0 dx2 with: w x() = C1 sinhλx + C2 coshλx + C3 sinλx + C4 cosλx Put the resulting four equations in matrix form w 0 2 () = 0  0 1 0 1  C1  0 dw dx2 () = 0  0 1 0 −1      0 C2  0    =   () = 0 sinhλl coshλl sinλl cosλl  C3  0 w l  dw sinhλl coshλl −sinλl −cosλl C4  2 0     l dx2 () = 0 Solution of determinant matrix generally yields values of λ which then yield frequencies and associated modes (as was done for multiple mass systems in a somewhat similar fashion) Paul A. Lagace © 2001 Unit 23 - 8