NMR Free Induction Decay: Bloch Equation Simulator

Nuclear magnetic resonance works because a static field B₀ makes nuclear spins precess at the Larmor frequency, and a resonant RF pulse can tip the sample's net magnetization away from equilibrium. This simulator renders that bulk magnetization vector in 3D exactly as the Bloch equations describe it: a chosen flip-angle RF pulse rotates it out of alignment with B₀, after which it precesses and relaxes back — Mz recovering with time constant T₁, the transverse component Mxy decaying with time constant T₂ — while a live strip chart traces the resulting free induction decay signal, the same waveform an NMR receiver coil actually detects and Fourier-transforms into a spectrum.