Low-field NMR (LF-NMR) is usually used as an analytical technique, for instance, to determine water and oil contents. For this application, no attempt is made to understand the physical origin of the data. Here we build a physical model to explain the five fit parameters of the conventional free induction decay (FID) for glassy oligosaccharide/water mixtures. The amplitudes of the signals from low-mobility and high-mobility protons correspond to the density of oligosaccharide protons and water protons, respectively. The relaxation time of the high-mobility protons is described using a statistical model for the probability that oligosaccharide hydroxyl groups form multiple hydrogen bonds. The variation of energy of the hydrogen bond is calculated from the average bond distance and the average angle contribution. Applying the model to experimental data shows that hydrogen atoms screen the water oxygen atoms when two water molecules solvate a single hydroxyl group. Furthermore, the relaxation time of the oligosaccharide protons is independent of its molecular weight and the water content. Finally, inversion of the FID using the inverse Laplace transform gives the continuous spectrum of relaxation times, which is a fingerprint of the oligosaccharide.