The chemical diagnostic tool of nuclear magnetic resonance uses a static magnetic field B₀ = B₀ẑ and a small-amplitude radio-frequency magnetic field B₁(t) to orient and manipulate nuclear spins in solids and liquids. To get a flavor for the manipulation, letbe the equation of motion for a nuclear magnetic moment m. Also let M_x(t) and M_y(t) be the transverse components of m in a coordinate system that rotates with B₁. If Ω_L = γB₀ is the Larmor frequency, show that and discuss the trajectory of the moment in the rotating and laboratory frames when ω = Ω_L.

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B₁ (t) = B₁ (x cos wt - y sin oot) and let m = ym x (Bo + B₁)