A power system stability is essential for maintaining the power system oscillation frequency within a small and acceptable interval around its nominal frequency. Hence, it is necessary to study and control the frequency for stable operation of a power system by knowing the characteristics within a power system. One approach is to understand the effectiveness of frequency and damping characteristics of generators in power systems. Hence, the simulation analysis of IEEE 118-bus power system is used for this study. The analysis includes theoretical analysis with a mathematical approach and simulation studies of swing equation to determine the characteristics of damped single-machine infinite bus, which is represented as a generator connects to a large network system with a small signal disturbance by line losses. Additionally, mathematical derivation of Prony analysis is presented in order to estimate the frequency and damping ratio of the simulation results. In the end, the results demonstrate that the frequency and damping characteristics of generators are highly dependent on the system inertia constant. Therefore, the higher inertia constant is a critical factor to ensure the system is more stable.