The structure and vibrational states of a prototype adsorbate-substrate system-carbon monoxide on the copper (001) surface-have been calculated from first principles within local density functional theory. Three CO coverages have been examined: theta = 0 (bare surface), 0.5, and 1. These systems are represented by a well converged slab model within which all atomic degrees of freedom are treated on an equal footing. The computed structural relaxations and vibrational frequencies are generally in excellent quantitative agreement with the available experimental measurements. The full monolayer is found to be energetically favorable to the half monolayer plus free CO molecule. This indicates that the maximum stable coverage is greater than theta = 0.5, in agreement with experiment. The vibrational analysis reveals that resonant coupling between adsorbate and substrate motions has a profound effect on the vibrational spectra, for example, the low-frequency, in-plane frustrated translational motion of the CO molecules mixes with long-wavelength copper phonons to form a broad resonance peak. This implies a finite lifetime which, for the half-monolayer system, is computed to be 3.0 ps, in excellent agreement with the measured value of 2.3 +/- 0.4 ps. For the full-monolayer system, the predicted lifetime is 0.7 ps; however this system is presently inaccessible to experiment. Resonant coupling is also found to affect the Rayleigh wave of the copper (001) surface. At half-monolayer CO coverage, this mode resonantly mixes with bulk copper phonons developing a finite lifetime, which is predicted to be 5.2 ps. To our knowledge, the lifetime of this mode has never been measured. For the fully covered surface, the Rayleigh wave does not form a resonance because the phonon coupling is forbidden by symmetry.