= Free three-mass spring chain
{title2=$\omega^2=0,\ k/m,\ (1+2/\alpha)k/m$}
For free-end <masses> $m,\alpha m,m$ joined by two identical <springs>, the displayed squared <frequencies> have displacement vectors $(1,1,1)$, $(1,0,-1)$ and $(1,-2/\alpha,1)$. Distinct <eigenvectors> are <orthogonal> in the <mass> <inner product>. The zero mode carries translation, while the middle <mass> does not move in the antisymmetric internal mode. Fixed end <springs> would give a different spectrum.
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