Transfer Function from Step Response

Correct Answer

C — s

Concept and Reasoning

For a unit-step input, R(s)=1/s. If the output is δ(t), then Y(s)=1. Hence G(s)=Y(s)/R(s)=s. Equivalently, the impulse response is the derivative of the step response.

Calculation / Key Relation

G(s)=Y(s)/R(s)=1/(1/s)=s

Exam Takeaway

Unit step in → multiply Y(s) by s to obtain G(s).

Common Mistake

Do not mistake the output transform Y(s) for the transfer function.