= Pivot-driven two-mass spring antiresonance
{title2=$\omega_0^2=k/m$}
Two identical vertical springs connect a driven pivot to two equal masses in sequence. After subtracting the static gravitational equilibrium, the laboratory displacement equation is $m\ddot{\mathbf x}+k\begin{pmatrix}2&-1\\-1&1\end{pmatrix}\mathbf x=k(z,0)^{\mathsf T}$. For $z=z_0\cos\omega_0t$ and $\omega_0^2=k/m$, a particular solution is $\mathbf x=(0,-z_0\cos\omega_0t)^{\mathsf T}$. Thus the upper mass has zero driven response even though this frequency is not an eigenfrequency. The general solution also contains both free <normal modes>.
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