GATE 2015 EE (EE2) – Question 63

Control Systems · Transient and Steady-state analysis of linear time invariant systems · 2 marks · Multiple choice

Which graph is the unit-step response of $G(s)=(1-2s)/(1+s)$?

Diagram for GATE 2015 EE (EE2) question 63

Option A in the figure
Option B in the figure
Option C in the figure
Option D in the figure

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (A) Option A in the figure

Explanation

For a unit step, Y(s)=(1−2s)/[s(s+1)]. Partial fractions give Y=1/s−3/(s+1).

Thus y(t)=1−3e⁻ᵗ for t≥0. It jumps initially to −2, then rises monotonically to 1. Only graph **A** has those initial and final values and that shape. The instantaneous jump comes from the transfer function's nonzero direct-feedthrough term.

More Transient and Steady-state analysis of linear time invariant systems questions

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…
GATE 2023 EE Q14 – Consider a unity-gain negative feedback system consisting of the plant G(s) (given below)…

All Transient and Steady-state analysis of linear time invariant systems questions →