= Continuous-wave nuclear magnetic resonance
For constant drive, set the three <rotating frame> derivatives to zero. Substitution first gives $u=\Delta T_2v$, then $w=M_0-\omega_1T_1v$, hence
$$
v=\frac{\omega_1T_2M_0}{1+\Delta^2T_2^2+s},\qquad
s=\omega_1^2T_1T_2.
$$
The absorption is proportional to $\omega_1v$. With $s\ll1$, its frequency dependence is a <Cauchy distribution> profile, often called a Lorentzian. With appreciable $s$, the response broadens and $w=M_0/(1+s)$ on resonance: <nuclear magnetic resonance saturation> limits the response. The short-pulse amplitude in the previous example is not a weak continuous drive; these are different operating regimes of the same equations.
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