Again assume a solution which has harmonic motion. It now has mulc all 2 MT-1620 components where o are the natural frequencies of the system and」 a is a vector of constants = J4 Substituting the assumed solution into the matrix set of governing equations →-02mAem+kAe01=0 o be true for all cases k-02m (224 This is a standard eigenvalue problem Either ( trivial solution) Paul A Lagace @2001 Unit 22-3i t ω ω MIT - 16.20 Fall, 2002 Again assume a solution which has harmonic motion. It now has multiple components: ω q t() = Ae (22-3) ~ ~ where ω are the natural frequencies of the system and:  M    A is a vector of constants = ~ Ai     M  Substituting the assumed solution into the matrix set of governing equations: it ⇒ −ω2 mA e + kA e it = 0 ~~ ~ ~ ~ To be true for all cases: [ k − ω2 m ] A = 0 (22-4) ~ ~ ~ ~ This is a standard eigenvalue problem. Either: A = 0 (trivial solution) ~ or Paul A. Lagace © 2001 Unit 22 - 3