Carbamazepine cocrystals with nicotinamide, saccharin and fumaric acid were synthesized and characterized by time-domain terahertz spectroscopy. Lattice vibrations of cocrystals with their individual constituents were investigated by means of the dispersion-corrected density functional theory with and without cell parameter constraints. The simulated THz spectra successfully reproduce the features of all the crystals in their experimental spectra. A better agreement between experimental and theoretical THz spectra is achieved when the cell parameter constraints are applied in geometry optimization. Some intensive modes of neat carbamazepine and cocrystals were discussed in terms of the motions of hydrogen bonds. The effect of lattice vibration on these cocrystallizations was further examined to gain insights into the thermodynamics. It is found that lattice vibration is favorable for all these cocrystal formations.