= Normal modes of two equal masses between three springs
For equal masses $m$, wall-spring constants $k_1,k_2$, and coupling-spring constant $k_3$, the <small-oscillation mass and stiffness matrices> are
$$
\mathsf M=mI,
\qquad
\mathsf K=
\begin{pmatrix}
k_1+k_3&-k_3\\
-k_3&k_2+k_3
\end{pmatrix}.
$$
If $k_1=k(1+\varepsilon\delta)$, $k_2=k(1-\varepsilon\delta)$, and $k_3=k\varepsilon$, the squared normal frequencies are
$$
\omega_\pm^2=\frac{k}{m}
\left[1+\varepsilon\left(1\pm\sqrt{1+\delta^2}\right)\right].
$$
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