Extensive new temperature-dependent LEED I/V data of the well-known (3x3)R30 o -CO structure and of the (2x2)-(O+CO) coadsorbate structure on Ru(0001) have been obtained down to 27K and analysed in terms of the thermal vibrations of the CO molecule, both by tensor low energy electron diffraction (LEED) with isotropic vibrations and by a scheme based on probability density functions including anisotropic vibrations. In both structures the CO molecule occupies the top site, as has been shown by previous LEED I/V analyses. In the coadsorbate structure this top site is surrounded by three oxygen atoms on hcp sites and the molecule is tilted by about 13 o in a direction away from one of the oxygen atoms. The different treatments agree on all aspects of geometry and vibrations, and also with earlier results where overlap exists. We show that in the coadsorbate system the thermal vibrational amplitudes are much smaller than in the single adsorbate system, and that the tilt of the CO molecule found there is mainly of static nature. Around this axis the static lateral displacement of the oxygen atom of CO increases from 0.23 9 at 27K to 0.31 9 at 350K and the vibration amplitudes increase from 0.08 9 to 0.11 9. The motion at the lowest temperature corresponds to the zero point motion. For the pure CO system the corresponding mean vibrational displacement of the O, which are now symmetric around the normal direction, range from 0.16 9 at 27K to over 0.4 9 at 350K. We conclude that low temperature measurements improve the accuracy of geometry determination by LEED I/V, and that temperature-dependent LEED can well be used for the determination of vibrational amplitudes. A corroboration of the reliability of LEED geometries is deduced from our extensive comparisons.