Protons that are in different chemical species, such as the CH2 and CH3 groups in fat, will resonate at slightly different frequencies due to local shielding of the static field by the electronic environment. This change in the resonance frequency is called chemical shift; it has made NMR an indispensable tool for chemists and physicists. If N species are present in the sample, and we neglect all interactions between nuclei, the FID is composed of a set of N decaying oscillators. Write down an equation that gives an expression for the transverse magnetization under these circumstances.
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