mechanics

Coupled Oscillators

Watch energy slosh between two spring-coupled masses in 3D. Discover normal modes — symmetric and antisymmetric oscillations that underpin molecular vibrations and phonons in crystals.

Coupled Osc.

A-Level

When two oscillators are coupled (e.g. by a spring), energy transfers back and forth between them. The system exhibits two normal modes: in-phase (symmetric) and out-of-phase (antisymmetric), each with its own frequency.

Mass1.0kg

Spring k30N/m

Coupling k5N/m

Amplitude 12.0m

📐 Formulas

m\ddot{x}_1 = -kx_1 + k_c(x_2-x_1)For mass 1

\omega_s = \sqrt{\frac{k}{m}},\; \omega_a = \sqrt{\frac{k+2k_c}{m}}Symmetric and antisymmetric frequencies

📋 Syllabus

AQA3.6.1.4

OCR5.3.2