Coupled Oscillators
Interactive simulation — adjust parameters and watch the visualization update in real time.
Live graphs
How it works
Two equal masses sit between identical outer springs and share a middle coupling spring. Small displacements from equilibrium obey coupled linear equations with two normal-mode frequencies: a symmetric mode at ωₛ = √(k/m) and an antisymmetric mode at ωₐ = √((k+2K)/m). A general initial condition superposes both, producing beats in the individual mass motions.
Key equations
mẍ₁ = −k x₁ − K(x₁ − x₂) · mẍ₂ = −k x₂ − K(x₂ − x₁)
ωₛ = √(k/m) · ωₐ = √((k + 2K)/m)