= Support-driven unequal-mass spring antiresonance
{title2=$\omega_0^2=k/m$}
For masses $m,2m$ connected in sequence to a moving support by springs $k,2k$, displacement coordinates give $m\operatorname{diag}(1,2)\ddot{\mathbf x}+k\begin{pmatrix}3&-2\\-2&2\end{pmatrix}\mathbf x=k(f,0)^{\mathsf T}$. The squared normal-mode frequencies are $(k/m)(2\pm\sqrt3)$. For support motion $f=F\sin\omega_0t$ with $\omega_0^2=k/m$, the negligible-damping steady response is $(0,-F\sin\omega_0t/2)$. The first mass has a response zero between the two resonances. Finite damping generally makes that zero imperfect.
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