© 2019 IEEE.When exposed to a damped oscillation, a mechanical system destructs exergy while reducing the energy efficiency of the system through entropy generation. Thus, entropy generation rate (EGR) in a mechanical system undergoing a damped oscillation is necessarily to be investigated for efficient handling. A mechanical system consisting of a cart with slender rod is considered in this work for EGR via a thermodynamic analysis. The dynamic model of the system is formulated using Lagrange's equations and afterwards it is linearized for small rotation of the rod. EGR is then introduced as the time derivative of the net work potential of the system. Finally, EGR is simulated for different initial conditions and a parametric study is performed to examine the effect of different parameters such as damping and stiffness on the entropy production. It is found that, the stiffness and initial conditions have direct effect on EGR. In this case, increasing either property increases EGR, however, no general trend is observed for the effect of damping due to the coupled nature of the system.