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The transfer function H(s) = 1/(s+a) corresponds to a first-order LTI system with a step response that reaches 63.2% of final value at which time?
At = ln(a) seconds always
Bt = a seconds (proportional to pole)
Ct = 2π/a seconds (one period)
Dt = 1/a seconds (one time constant)
Answer & Solution
Correct answer: D. t = 1/a seconds (one time constant)
Step response: (1/a)(1 - e^{-at}). At t = τ = 1/a, value is (1/a)(1 - e^{-1}) ≈ 0.632/a. The time constant τ = 1/|pole|.
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