The dynamics of the low-frequency vibrational modes of microtubules play a key role in many theoretical models regarding their biological function. We analyze these dynamics through large scale, classical molecular dynamics simulations of a microtubule composed of 42 tubulin heterodimers to provide insights into the qualitative nature of the vibrational energy absorption and dissipation mechanisms. The computed microtubule absorption spectra and vibrational density of states in the terahertz regime are presented, along with an analysis of the vibrational dephasing rates of the tubulin monomer center of mass dynamics, which are shown to be overdamped. Additionally, the presence of the microtubule modifies the dynamical properties of the solvation shell structure within roughly 10 angstrom of the protein. These vibrational properties are similar to those seen in other globular proteins and indicate microtubules are unlikely candidates for any large scale collective vibrational processes in the terahertz regime such as Frohlich condensates.