In the following problem, find the natural frequencies of the three-mass system of Fig (Attached), using the given masses and spring constants. For each natural frequency ω, give the ratio a 1 :a 2 :a...

In  the following problem, find the natural frequencies of the three-mass system of Fig (Attached), 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
D k₄
=2