Final answer:
To find the impulse response of an LTI system given its step response, differentiate the step response. For a circuit with an inductor and resistor, the self-inductance can be found using L = √√I(1 + m₁)h formula, taking into account the appropriate value for m₁.
Step-by-step explanation:
The question relates to finding the impulse response of a Linear Time-Invariant (LTI) system given its step response. To compute the impulse response, it is necessary to differentiate the step response with respect to time, as the step response is the integral of the impulse response. A common LTI system is an electric circuit consisting of an inductor (L) and a resistor (R) in series.
A good approach for calculating the self-inductance of an inductor consists of using the given information and understanding that inductance L can be calculated using the formula L = √√I(1 + m₁)h, where √√I is the square root of the moment of inertia, m₁ is a dimensionless multipole moment (0, -1, or +1 in our case), and h is a constant. Since the question suggests we are given 1 = 1, the solution to find L involves determining the appropriate value for m₁ and applying it to the formula.