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(1 point) Consider the following spring system. 3000 m, Зcy -0000000000 ma (1 = ģ, c = 1, c3 = ģ, c4 = 1 1 m2 = = } mi = 3 -1 Write the stiffness matrix K -1 2 9 -3 Write the matrix M-K -2 4 Find the eigenvalues and eigenvectors of M-1K 1 • Smaller eigenvalue = 3 with eigenvector 2 3 • Larger eigenvalue = 10 with eigenvector -1
If this spring system oscillates without any external forces present, then the position of each mass satisfies the following general formula: u(t) = (aj cos ( t) + b sin t)) + (az cos ( t) + b2 sin t)) If the system begins oscillation with initial position u(0) = 00 and initial i velocity w'(0) = (1) then the position of the masses at time t is given by ui(t) = U2(t) =
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