A structure with a mass moving on it constitutes a classical coupled time-varying system. A dynamic model of a coupled moving-mass and simply supported beam time-varying system is built. The influence of the moving-mass velocity and acceleration is analyzed, and the damping induced by the moving mass is obtained through numerical simulation. An experimental system consisting of a simply supported beam and a moving mass sliding on it is set up. The initial damping of the experimental system is determined based on the baseline experiment. Different modal parameter estimation methods in the frequency and time domain are employed to estimate natural frequencies of the experimental system with different moving-mass velocities. The results indicate that the dynamic model can accurately describe the moving mass problem. This experimental system can be used to validate theoretical studies on dynamics, especially the modal parameter estimation of time-varying structures.