Normal modes of three symmetrically coupled trapped masses
= Normal modes of three symmetrically coupled trapped masses
For three unit masses with unit springs between every pair and one unit spring anchoring each mass to the origin,
$$
M=I,\qquad K=4I-J,
$$
where $J$ is the all-ones matrix. The collective mode $(1,1,1)$ has angular frequency $1$, while the two-dimensional sum-zero subspace has angular frequency $2$.