GATE 2015 EE (EE2) – Question 34

The unit-impulse response of an open-loop LTI system is $e^{-2t}(\sin5t+\cos5t)$ for t≥0. Its DC gain is ________.

Show answer and explanation

Correct answer: 0.23 to 0.25

Explanation

The transfer function is the Laplace transform of the impulse response. Its sine and cosine terms give $G(s)=5/[(s+2)^2+25]+(s+2)/[(s+2)^2+25]$.

At s=0, DC gain is (5+2)/(4+25)=**7/29≈0.241379**, in 0.23–0.25. This is also the integral of the impulse response over nonnegative time.

GATE 2015 EE (EE2) Q63 – Which graph is the unit-step response of G(s)=(1-2s)/(1+s)?
GATE 2026 EE Q13 – The Laplace transform of the step response of a system is given by Y(s)=100s(s+100) The…
GATE 2025 EE Q22 – Selected data points of the step response of a stable first-order linear time-invariant…
GATE 2024 EE Q21 – Consider the standard second-order system of the form n2s2+2 ns+ n2 with the poles p and…
GATE 2024 EE Q22 – Consider the cascaded system as shown in the figure. Neglecting the faster component of…
GATE 2024 EE Q58 – Consider the stable closed-loop system shown in the figure. The asymptotic Bode magnitude…