Register

GATE Electrical 2016 Set 2 | Question: 4

• retagged by
322 views
0 0 votes

Consider a causal $LTI$ system characterized by differential equation $\frac{dy(t)}{dt}+\frac{1}{6}y(t)=3x(t)$ The response of the system to the input $x(t)=3e^{-\frac{t}{3}}u(t)$, where $u(t)$ denotes the unit step function, is

  1. $9e^{-\frac{t}{3}}u(t)$
  2. $9e^{-\frac{t}{6}}u(t)$
  3. $9e^{-\frac{t}{3}}u(t)-6e^{-\frac{t}{6}}u(t)$
  4. $54e^{-\frac{t}{6}}u(t)-54e^{-\frac{t}{3}}u(t)$

Please log in or register to answer this question.

Voting & Accepting an answer helps improve the community

Related questions

0 0 votes
0 0 answers
278
278 views
Misbah Ghaya asked Jan 29, 2017
278 views
GATE Electrical 2016 Set 1 | Question: 4
A function $y(t)$, such that $y(0)=1$ and $y(1)=3e^{-1}$, is a solution of the differential equation$\dfrac{d^{2}y}{dt^{2}}+2\dfrac{dy}{dt}+y=0$. Then $y(2)$ is$5e^{-1}$$...
0 0 votes
0 0 answers
266
266 views
Arjun asked Feb 26, 2017
266 views
GATE Electrical 2017 Set 1 | Question: 30
Let a causal LTI system be characterised by the following differential equation, with initial rest condition$\frac{d^{2}y}{dt^{2}}+7\frac{dy}{dt}+10y (t)=4x(t)+5\frac{dx(...
0 0 votes
0 0 answers
405
405 views
Misbah Ghaya asked Jan 29, 2017
405 views
GATE Electrical 2016 Set 2 | Question: 30
Let $y(x)$ be the solution of the differential equation $\frac{d^{2}y}{dx^{2}}-4\frac{dy}{dx}+4y=0$ with initial conditions $y(0)=0$ and $\frac{dy}{dx}\mid _{x=0}=1$ Then...
0 0 votes
0 0 answers
242
242 views
Misbah Ghaya asked Jan 29, 2017
242 views
GATE Electrical 2016 Set 2 | Question: 8
The solution of the differential equation, for $t 0, y"(t)+2y'(t)+y(t)=0$ with initial conditions $y(0)=0$ and $y'(0)=1$, is ($u(t)$ denotes the unit step function),$te^...
← Previous · GATE Electrical 2016...Next → · GATE Electrical 2016...
← Previous in category · GATE Electrical 2016...Next in category → · GATE Electrical 2016...
Position:
Show:
Answer: