The simplified model was established for the dual-degree-of-freedom tilted support spring system. Then, the equations of the key components were obtained under the post-peak-sawtooth wave. To investigate the influence of the support angle and other parameters on the damage evaluation of the key components, the Runge-Kutta method was used to solve the equations, and the damage boundary curves and surfaces were plotted using the critical acceleration and the critical velocity as coordinates. The results show that as the frequency ratio increases, the size of the damage zone decreases and the size of the safety zone increases, while reducing the support angle, or increasing the amplitude of the dimensionless peak pulse and the mass ratio can increase the size of the safety zone. In addition, the support angle generally is controlled within 70°~90°. Therefore, by controlling these parameters, the impact resistance of the key components can be improved.