Understanding the state of the hydration water in cement and the ways to control it are likely to be the keys to the improvement of its ultimate strength and durability. In this study we investigate the diffusional dynamics of water molecules in hydrated tri-calcium silicate, a major component in ordinary Portland cement. The spectra of incoherent quasi-elastic neutron scattering from hydrogen atoms were measured using a high-resolution chopper spectrometer having an energy resolution of 28 μeV. The spectra were analyzed by using two different methods: (i) an explicit dynamical model, recently proposed by us, taking into account the existence of two types of water: ``immobile water'', presumably water bound inside the colloidal particle component of the cement paste, and ``glassy water'', water imbedded in the gel-like component filling the spaces between the colloidal particles, and (ii) a new method in which we analyze the susceptibility function in the frequency domain instead of dealing with the dynamic structure factor as in (i). We extract three important parameters: the Q-independent fraction of immobile water p;the Q-independentstretch exponent β (or b) and the Q-dependentaverage relaxation time τ (or 1/ωp) of the glassy water. Both methods account very well for the cement hydration process, but the second method is intuitively more appealing and simpler.