Dynamical response of a spin system to the sudden application of a constant magnetic field

The Krylov–Bogolyubov–Mitropol'skii method of averaging is used to consider oscillations of the longitudinal magnetization which arise after the sudden application of a constant magnetic field. It is shown that oscillations are observed at frequencies which are multiples of the Zeeman frequency and they are damped with characteristic time $T_2\sim 1/\omega_\alpha$ (where $\omega_\alpha$ is the characteristic frequency associated with the dipole-dipole interaction). The proposed method can also be directly applied to describe other transient processes in magnetic resonance.