Previous Year Question
If the unit step response of a system is a unit impulse function, then what will be the transfer function of the system?
Correct answer: C
Explanation
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.
Formula
G(s)=Y(s)/R(s)=1/(1/s)=s
Step-by-step solution
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.
Common mistake
Do not mistake the output transform Y(s) for the transfer function.
Exam tip
Unit step in → multiply Y(s) by s to obtain G(s).
Quick method
Unit step in → multiply Y(s) by s to obtain G(s).