In this study, we aim to propose tuned mass dampers with initial displacement that are possible to control impulsive seismic responses effectively for architectural structures. In advance of the study on control of seismic responses, we aim to propose design formulas to control the structural responses subjected to impulse forces. In our previous study, we have proposed the design formulas using the optimal tuning and damping ratios for harmonic ground vibration. But to improve control effect on overall time history responses is difficult, because these formulas are based on the principle of the beating phenomenon. Then, in this paper, we focus on the vibration property when the damping ratio of the tuned mass damper is larger than that of our previous study and propose new design formulas with high control effect on impulse forces. Moreover, we propose design formulas considering the damping of the structure.