目前的大学物理教材中，关于阻尼振动部分的编撰方式给缺乏微分方程理论背景的学生带来了一定的认知负荷.以面向物理学专业本科生的普通物理课程为例，其教学方法虽然通过演绎推理降低了一定的数学要求.然而，临界阻尼形式解的特殊性，使其仍无法较好地、自然地融入教学过程中.本文首次提出了一种利用极限法求解临界阻尼状态的新颖推导方法及相应的教学思路.这种创新的求解过程及教学思路，不仅有助于培养物理学专业本科生的科学思维与创新能力，同时也可作为面向非物理专业理工科学生在阻尼振动部分进行拓展教学的补充素材.

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.