This note presents a beam dynamics analysis of a possible muon cooling experiment based on 88 MHz cavities. The proposed set-up is a subsection of the cooling channel in the CERN reference scheme for a neutrino factory. We present two different set-ups using 8 and 4 cavities. For each of these set-ups we have carried out a beam dynamics study based on engineering designs for the cavities and solenoids. The study includes a parameter scan which allows to evaluate the performance of the systems for various input beam parameters and settings