Normal Modes

Coupled oscillators and standing wave patterns

Normal modes are the independent oscillation patterns of a coupled system — each mode oscillates at a distinct frequency with all parts moving in phase or exactly anti-phase. Any arbitrary motion can be written as a superposition of normal modes. For a string, normal modes are harmonics (standing waves). For coupled pendulums, the two modes are in-phase (lower frequency) and out-of-phase (higher frequency). This concept extends to quantum mechanics (phonons) and molecular vibrations.