Implementing second-order low-pass filters in audio systems is crucial in refining audio signals by eliminating undesirable high-frequency noise. These filters typically involve second-order op-amp circuits configured as voltage followers, encompassing two nodes with distinct storage elements.

The analysis of such circuits follows a systematic approach, similar to the second-order RLC circuits. In practical scenarios, bulky inductors are rarely employed due to their size and weight. This means the focus here is primarily on RC second-order op-amp circuits, which have extensive applications in devices like filters and oscillators.

Two differential equations emerge after applying Kirchhoff's current law at the nodes. Furthermore, a second-order characteristic differential equation is deduced by observing voltage relationships across the circuit components. This equation embodies both transient and steady-state responses.

The transient response gradually diminishes over time and shares resemblances with the solutions found in source-free circuits, exhibiting characteristics of overdamped, underdamped, and critically damped scenarios. Once the circuit achieves a steady state, the capacitors and resistors no longer conduct current, and the ideal op-amp input terminals block current flow. Consequently, the steady-state response matches the source voltage.

Notably, eliminating the input source voltage leads to a pure transient response. These second-order op-amp circuits have diverse applications in enhancing audio quality and are pivotal in various audio processing systems. Understanding their behavior under different damping scenarios aids in achieving optimal audio signal refinement.