Coupled Oscillators

This interactive simulator explores Coupled Oscillators in Classical Mechanics. Two masses, three springs: normal modes ωₛ, ωₐ and beats. Use the controls to change the scenario; watch the visualization and any graphs or readouts to connect the model with lectures, labs, and homework.

Who it's for: Best once you already know the basic definitions and want to build intuition. Typical context: Classical Mechanics.

Key terms

  • coupled
  • oscillators
  • coupled oscillators
  • mechanics
  • classical

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)