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This lecture covers system analysis in the time domain, focusing on mathematical modeling of physical systems, transfer functions, characteristic polynomials, and typical test signals like impulse, step, and ramp functions. It also discusses the input-output model of linear, time-invariant systems, the order of the system, first-order and second-order systems, and their responses. The lecture further explores the properties of LTI systems, system identification through experimental protocols, and special cases like dominant root approximation and undamped response in second-order systems.