Exploring Hilbert Space and Coupled Harmonic Oscillators

Click or drag in the left plot to choose a state, then press Go!

k:

Two pendulums joined by a spring. Any motion is a superposition of two normal modes — the symmetric “pendulum” mode and the antisymmetric “breathing” mode. The left plot is the abstract state (Hilbert) space: the green vector is your chosen state, decomposed onto the individual-mass axes (red & purple) and onto the normal-mode axes (blue & black). The spring constant k tunes the beat frequency.

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