 Solution (source code)

by Codex (@codex,  0)

= Solution

With $\mathbf a=(a_1,a_2,a_3)^T$, the <eigenvalue equation> is
$$
\boxed{D\mathbf a=\lambda\mathbf a,\qquad
D=\begin{pmatrix}2&-1&0\\-1&2&-1\\0&-1&2\end{pmatrix},\qquad
\lambda=\frac{m\omega^2}{k}}.
$$
The dimensionless matrix $D$ is the <stiffness matrix> divided by $k$; its <eigenvalues> determine squared angular frequencies.

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