The mechanism and prevention of coal burst is an important issue in the study of coal mine dynamic disasters. The disturbance of surrounding rocks can trigger the quasi-resonance phenomena of roadway roof support system in close proximity to its resonant state, ultimately inducing impact disasters. This is manifested in three strong quasi-resonant responses, including roof displacement, velocity and acceleration. Based on the support instability and plastic buckling criteria, three safety factors and the corresponding dangerous disturbance frequency ratio interval for the dynamic failure of support are proposed, and the support damping control strategy is given, aiming at the impact disasters induced by the quasi-resonance of the roof support system. The results show that when the amplitude of disturbing force is lower than the critical failure force of the support under static loads, the quasi-resonant phenomena of roof support system is the main reason for the dynamic failure of support. The frequency ratio range of quasi-resonant dangerous disturbance for support failure is related to the damping ratio and force-amplitude ratio of roof support system. With the increasing damping ratio, the displacement, velocity and acceleration response amplitudes at the roof quasi-resonance will decrease. The support damping is a controlling factor sensitive to these three types of quasi-resonant responses. When the damping ratio in the roof support system increases or the force- amplitude ratio (the ratio between the amplitude of external disturbance and the critical load for static support failure) decreases, the dangerous disturbance frequency ratio interval of the support will narrow or even disappear. When the damping ratio and force-amplitude ratio are small, the dangerous disturbance frequency ratio intervals of the roof support system under three quasi-resonant conditions are close. This study will enrich the understanding of the mechanism behind coal bursts and provide valuable insights for the design of support control.