Mechanical vibration control and second-order LTI system analysis of an SDOF with harmonic motion

It is critical to analyze vibration because of the prevalence of vibration in engineering. Our primary objective is to find a new method to analyze mechanical system vibrations under different circumstances with a single degree of freedom (SDOF). The mass-spring-damping (MSD) system's mathematical structure will be used as a baseline for analyzing the SDOF system. The second-order homogeneous linear time-invariant (LTI) system (under-damped, critically-damped, and overdamped) is analyzed and given in this conference paper. The findings include identified parameters such as dynamic magnetic variables and step responses. Besides, a PID controller is optimized for vibration.