MT-1620 al.2002 For each eigenvalue, the homogeneous solution is e sina. t coSO. t homogeneous Still an undetermined constant in each case(An ) which can be determined from the initial conditions Each homogeneous solution physically represents a possible free vibration mode Arrange natural frequencies from lowest (o, to highest (o By superposition, any combinations of these is a valid solution Example: Two mass system(from Unit 19) Figure 22.1 Representation of dual spring-mass system Paul A Lagace @2001 Unit 22-6MIT - 16.20 Fall, 2002 For each eigenvalue, the homogeneous solution is: r r r q i hom = φi () e iω r t = C1 φi () sinωr t + C2 φi () cosωr t ~ ~ ~ ~ homogeneous Still an undetermined constant in each case (An) which can be determined from the Initial Conditions • Each homogeneous solution physically represents a possible free vibration mode • Arrange natural frequencies from lowest (ω1) to highest (ωn) • By superposition, any combinations of these is a valid solution Example: Two mass system (from Unit 19) Figure 22.1 Representation of dual spring-mass system Paul A. Lagace © 2001 Unit 22 - 6