Final answer:
The impulse response of a system with an inductor and resistor can be derived from a triangular step response by calculating the area under the curve, in essence by differentiating the step response function over time.
Step-by-step explanation:
Calculating the impulse response of any dynamic system essentially means finding out how the system reacts over time to a brief input. In the context of electrical circuits, particularly one with an inductor (L) and a resistor (R), the impulse response helps in understanding how currents and voltages change when the circuit experiences a sudden electrical impulse.
The impulse response can be found by analyzing the step response of the system. For a triangular step response, the impulse is the derivative of the step response. If you have a triangular step response, its graph is in the shape of a triangle on a force versus time diagram. The impulse can be calculated by finding the area under the curve, which, for a triangle, is calculated as 0.5 × base × height. Three time constants after the circuit is completed imply that the system has sufficiently responded to the step input, and this would typically be the timeframe over which you measure the step response to then derive the impulse response.
For example, if a step response is defined by a piecewise function like 1.5t for 0≤ t < 2.0 ms, and so on, the impulse response would be the derivative of this function piece by piece. It should be noted that the units for the impulse would be newton-seconds (Ns) or, equivalently, kilogram meters per second (kg·m/s).