The GATE Grind

GATE 2019 EC – Question 15

Networks, Signals and Systems · LTI Systems · 1 mark · Multiple choice

Let $Y(s)$ be the unit-step response of a causal system having a transfer function

$$G(s)=\frac{3-s}{(s+1)(s+3)}$$

that is, $Y(s)=\frac{G(s)}{s}$. The forced response of the system is

  1. $u(t)-2e^{-t}u(t)+e^{-3t}u(t)$
  2. $2u(t)-2e^{-t}u(t)+e^{-3t}u(t)$
  3. $2u(t)$
  4. $u(t)$

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (D) $u(t)$

Explanation

$Y(s)=\frac{3-s}{s(s+1)(s+3)}=\frac1s-\frac{2}{s+1}+\frac{1}{s+3}$. The forced response is the part due to the input pole at $s=0$, which is $u(t)$ (the $e^{-t}$ and $e^{-3t}$ terms are the natural response).