Coupled Oscillators — Normal Modes & Beats

Presets

System

Number of masses (N) 2

Spring constant k 1.0

Coupling κ/k 0.30

Mass m 1.0

Damping γ 0.02

Initial Condition

Stats

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ω₁ (rad/s)

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ωₙ (rad/s)

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Kinetic E

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Potential E

Normal modes
ω²ₘ = (k/m)[1−cos(mπ/(N+1))]·2 for mode m=1..N. Coupled oscillators are the classical foundation of phonon dispersion in crystals and standing waves on a string.