We present first-principles molecular dynamics simulations, obtained at the density functional level of theory, for molecular vibrations of amino acids on copper surfaces. Specifically, we have studied the hydrogen-bonded networks formed by glycine and alanine on the Cu{110} and Cu{311} surfaces. Fourier transformation of the autocorrelation function in each case leads to frequency spectra that may be compared with data from infra-red absorption experiments, where available. Moreover, by separately Fourier transforming key structural parameters such as individual bond lengths or bond angles, it is possible to make confident band assignments that aid in the interpretation of experiment. By tracking the motion of atoms over time, it is also possible extract mean atomic positions, and realistic thermal ellipsoids, which may in turn be of use in understanding results from diffraction experiments and/or scanning tunneling microscopy.