In recent works [1],[4], it has been shown that the damping of a linear time invariant system relates to the so-called characteristic ratios (αk, k=1,…, n-1) which are defined by coefficients of the denominator of the transfer function. However, the exact relations are not yet fully understood. For the purpose of exploring the issue, this paper presents the analysis of time response sensitivity to the characteristic ratio change. We begin with the sensitivity of output to the perturbations of coefficients of the system denominator and then the first order approximation of the αk perturbation effect is computed by an explicit transfer function. The results are extended to all-pole systems in order to investigate which characteristic ratios act dominantly on step response. The same analysis is also performed to a special class of systems whose denominator is composed of so called K-polynomial. Finally, some illustrative examples are given.