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This lecture delves into the critically damped response of a second-order system, analyzing the behavior of the system when the damping factor is equal to one. The instructor explains the responses of the system in detail, highlighting the significance of the steady-state gain and the exponential decay of certain terms. Through mathematical derivations and transformations, the lecture demonstrates how the system's response evolves over time, emphasizing the impact of the damping factor on the system's behavior.