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Vertical normal modes of two equal suspended masses

For equal masses

m

and spring constants

k

, vertical displacements from equilibrium have stiffness and mass matrices

K = k (2 - 1 - 1 1), M = m I .

The two squared frequencies and displacement ratios are

ω_{\pm}^{2} = \frac{k}{2 m} (3 \pm 5), \frac{η _{2}}{η _{1}} = \frac{1 \mp 5}{2} .

Gravity shifts the equilibrium but does not enter these vertical frequencies.

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