Solution
= Solution
In a <breathing mode>, each <displacement> is proportional to its equilibrium position. A representative <vector> is
$$
q_b=(-1,1,1,1,-1,-1,1,-1)^T.
$$
Multiplying by the <stiffness matrix> gives $Kq_b=4kq_b$. Thus
$$
\boxed{q\propto q_b,\qquad\omega^2=\frac{4k}m,\qquad\omega=2\sqrt{\frac km}.}
$$
Positive and negative amplitudes are uniform expansion and contraction about the center.