Free vibrating motion can take place in an acoustic media. This motion can be steady hence have constant periodic variations or unsteady and thus experience light damping or heavy damping. We give a modeled analysis of unsteady periodic motion of an oscillator in a cylindrical acoustic medium that allow such waves to be transmitted through them. This has been approached by calculating variation within the proposed boundary functions and boundary potentials. Limitations for these calculations have been done depending on the time, and how free oscillations are expected to behave in cylinder carrying a suspended mass. This work investigated motion by constructions that interact with their environment with the acoustic media. Since the dynamics considered here were very complex, modeling the system with one grade of free motion and applying different types of constructions whether ground, underground, cylindrical, spherical constructions and containers was considered. This work borrowed heavily on the modeling of seismic and blast waves as modeled with rigid inclusions containing elastically fastened mass interacting continuous solid medium. This study joined motion of any continuous medium with other discrete systems. The results displayed measurement systems for wave processes having interference at their eigen- frequencies just like those under seismic wave interactions and this work considered the result as similar to those in discrete systems.