In current college physics textbooks, the way of teaching the damped harmonic oscillation brings a certain cognitive load to students who lack a background in differential equation theory. Taking General Physics for undergraduates majoring in physics as an example, its modern teaching method has already reduced certain mathematical requirements through deductive reasoning. However, the exotic solution of critical damping problem makes it impossible to integrate into the teaching process naturally. In this paper, a new derivation method for solving the critical damping by using the limit method and its corresponding teaching methods is presented. This innovative solution process and teaching methodology not only help to cultivate the scientific thinking and innovation ability of physics undergraduates, but also can be used as supplementary material to expand the teaching of the damped harmonic oscillation for non-physics science and engineering students.