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Unit Impulse and Unit Step Response of Linear Differential Equations
The unit impulse response and unit step response show how a system reacts to a sudden kick or a steady push, and they are used to model things like a chemical tank or a mass on a spring. The unit impulse response solves the differential equation with a delta function (a unit-sized instant kick) on the right side and rest initial conditions. The unit step response solves it with a step function (zero before time zero, one after). Both tell you how a linear system with constant coefficients reacts to a sudden input.