Coupled Pendula
Normal modes and energy exchange via resonance
About: Two identical pendulums connected by a spring exhibit normal modes: the symmetric mode (both swing together, spring unstretched) at ω₋ = √(g/L), and the antisymmetric mode (opposing swing) at ω₊ = √(g/L + 2k/m). When only one pendulum is displaced, beats result — energy oscillates completely between pendulums with period T_beat = 2π/(ω₊−ω₋). This classical analogue of quantum tunneling appears in molecular vibrations, coupled LC circuits, and neutrino oscillations.