Purpose <p>In this paper, the transient response of typical low-degree-of-freedom systems is analyzed. The purpose of this research is to maximize the exponential time-decay rate (ETDR) of the system transient response, which is essential for the vibration attenuation.</p> Methods <p>A pole-location-based method is adopted to analyze the ETDR of vibrating primary systems with six inerter-based configurations. First of all, the maximum ETDR is optimized with respect to the damping parameter based on five pole location scenarios. Then, analytical analysis is employed to derive the optimal design of the tuning parameter. Furthermore, the optimal ETDR with respect to optimal damping and tuning parameters is obtained for any given inertance.</p> Results <p>Analytical results are given to demonstrate the effectiveness of the derived optimal designs. Compared with traditional tuned mass dampers (TMDs), several inerter-based configurations perform better in maximizing ETDR, and then the transient performance is enhanced. Moreover, it is proved that optimal designs are more appropriate for improving the transient performance than those in the previous investigations.</p> Conclusion <p>The results demonstrate that optimal designs for the maximum ETDR derived in this paper are effective in faster suppression of structure vibration.</p>