Electric drive systems are essential in various industries, and ensuring their trouble-free operation is crucial. Failure to analyze and diagnose vibrations in these systems can lead to significant failures, including accidents and fatalities, as exemplified by incidents in power plants and with electric submersible pumps. Experimental testing on actual systems is one approach, but it can be impractical due to various constraints. Therefore, mathematical models are often used to study system behavior. Mathematical models pertaining to mechanical objects, like transmission shafts, are typically described by sets of partial differential equations, which can be challenging to solve analytically and numerically. Linear models or linearization techniques are commonly used due to the complexity of nonlinear equations.