 Solution

ID: past-exam-of-the-mathematics-course-of-the-year-1-of-the-natural-sciences-course-of-the-university-of-cambridge/2015/paper-2/17/c/solution

With

a = (a_{1}, a_{2}, a_{3})^{T}

D a = λ a, D = 2 - 1 0 - 1 2 - 1 0 - 1 2, λ = \frac{m ω ^{2}}{k} .

The dimensionless matrix

D

is the stiffness matrix divided by

k

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