Inertial navigation system is an autonomous navigation system that does not rely on external information, which consists of an inertial measurement unit (IMU) and an inertial navigation algorithm. The performance of the laser inertial measurement unit(LIMU) directly affects the navigation accuracy of the space system. The design of conventional LIMU damping systems typically involves extensive vibration and impact testing at various magnitudes. This process requires constant parameter adjustments based on test results and ultimately, the parameters of the damping system are finalized, consuming significant human and material resources as well as time. This paper introduces a vibration response simulation algorithm for LIMU damping systems. The algorithm utilizes a precise kinetic model and motion equations of the LIMU damping system, solving the differential equations of the vibration damping system to obtain displacement, acceleration responses, and dynamic characteristics of the LIMU under various vibration and impact environments with different parameters. And this enables quantitative analysis of damping space and damping effects. This algorithm enables structural margin assessment, vibration magnitude estimation, and nonlinear dynamic characteristics evaluation for the LIMU. It provides a theoretical basis for the selection of product dampers and the design of damping systems, significantly reducing human, material, and time costs. The correctness of the algorithm has been demonstrated through its successful application in the design and parameter determination of a specific type of three-self-inertia group damping system and experimental data on impact and dynamic characteristics.