In each of Problems 41 through 46, use the spectral decomposition methods of this section to find a fundamental matrix solution x(t) = e^At for the linear system x' = Ax given in the problem.

Problem 25 in Section 7.5

Suppose that m = 75 slugs (the car weighs 2400 lb), L₁ = 7 ft, L₂ = 3 ft (it's a rear-engine car), k₁ = k₂ = 2000 lb/ft, and I = 1000 ft-lb-s². Then the equations in (40) take the form

Transcribed Image Text:

75x" + 4000x - 80000 = 0, 8000x + 116,0000 = 0. 10000"