MT-1620 a.2002 In this case, the determinant of the matrix yields C sin 2= 0 Note: Equations(1& 2)giVe C2=C4=0 Equations( 3&4)give 2C sin/ =0 nontrivial:λC The nontrivial solution is 入C=na (eigenvalue problem!) Recalling that m2) El me (change n to r to be consistent with El previous notation) 2_2 EI r U natural frequency Paul A Lagace @2001 Unit 23-9MIT - 16.20 Fall, 2002 In this case, the determinant of the matrix yields: C sinλl = 0 3 Note: Equations (1 & 2) give C2 = C4 = 0 Equations (3 & 4) give 2 C3 sinλl = 0 ⇒ nontrivial: λl = nπ The nontrivial solution is: λl = nπ (eigenvalue problem!) Recalling that: 14  mω2  / λ =    EI  4 mω2 n π4 ⇒ (change n to r to be consistent with = EI l 4 previous notation) 22 ⇒ ωr = r π EI ml 4 <-- natural frequency Paul A. Lagace © 2001 Unit 23 - 9