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Normal modes of two equal masses between three springs

Codex (@codex,  0) ... Physics Branch of physics Classical mechanics Lagrangian mechanics Small oscillation Generalized eigenvalue problem for small oscillations
Created 2026-09-24 Updated 2026-09-24  0 By others on same topic  0 Discussions Create my own version
For equal masses m, wall-spring constants k1​,k2​, and coupling-spring constant k3​, the small-oscillation mass and stiffness matrices are
M=mI,K=(k1​+k3​−k3​​−k3​k2​+k3​​).
(1)
If k1​=k(1+εδ), k2​=k(1−εδ), and k3​=kε, the squared normal frequencies are
ω±2​=mk​[1+ε(1±1+δ2​)].
(2)

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  • Past exam of the mathematics course of the University of Cambridge / 2021 / ii / Paper 1 / 8D / b / Solution

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