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 26 in Section 7.5

Suppose that k₁ = k₂ = k and L₁ = L₂ = 1/2L in Fig. 7.5.14 (the symmetric situation). Then show that every free oscillation is a combination of a vertical oscillation with frequency

and an angular oscillation with frequency

Transcribed Image Text:

2k/m = Im