Residual modes of vibration refer to the resonant vibrations that persist in a structure after a motion has ceased, influenced by the material's inertial and elastic properties. These modes are significant because they can contaminate predictions in simulations, such as those in FEM solvers like ANSYS and PAM Crash. In applications like lightweight manipulators and ultra-precision manufacturing, residual vibrations can limit performance, impacting operating time and positioning accuracy. Effective vibration reduction strategies, including passive isolators, are essential to mitigate low-frequency residual vibrations that can degrade machine accuracy. Understanding and addressing residual modes is crucial for enhancing system performance in various engineering applications.