MT-1620 al.2002 Can recast equation(23-6) to be w ma W (237) El The solution to this homogeneous equation is of the form Putting this into (23-7)yields 0 E m10 El So this is an eigenvalue problem (spatially). The four roots are p=+λ,-λ,+i,-i Where m10 E This yields Paul A. Lagace @2001 Unit 23-6MIT - 16.20 Fall, 2002 Can recast equation (23-6) to be: 4 d w mω2 dx 4 − w = 0 (23-7) EI The solution to this homogeneous equation is of the form: w x() = e px Putting this into (23-7) yields 4 px mω2 pe − e px = 0 EI 4 mω2 ⇒ p = EI So this is an eigenvalue problem (spatially). The four roots are: p = + λ, -λ, + iλ, - iλ where: 14  mω2  / λ =    EI  This yields: Paul A. Lagace © 2001 Unit 23 - 6