In Problems 12 and 13, find the natural frequencies of the three-mass system of Fig. 7.5.1, using the given masses and spring constants. For each natural frequency ω, give the ratio a₁:a₂:a₃ of amplitudes for a corresponding natural mode x₁ = a₁ cos ωt , x₂ = a₂ cos ωt , x₃ = a₃ cos ωt.

m₁ = m₂ = m₃ = 1; k₁ = k₂ = k₃ = k₄ = 1

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