GATE (TF) Textile 2017 Question Paper Solution

Table of Contents

Question 02 (Textile Engineering & Fibre Science)

The Laplace transform $e^{-t}cos(2t)$ is

(A)	$\frac{s-1}{s^2-2s+5}$
(B)	$\frac{1}{s^2+2s+5}$
(C)	$\frac{s+1}{s^2+2s+2}$
(D)	$\frac{s+1}{s^2+2s+5}$

Answer / Solution

$e^{-t}cos(2t)$
Laplace transform of cos(at) is $\frac{s}{s^2+a^2}$
and
Laplace transform of $e^{-bt}cos(at) is \frac{s+b}{(s+b)^2+a^2}$
Now Laplace transform of $e^{-t}cos(2t)$ is-
$\frac{s+1}{(s+1)^2+2^2}$
$\frac{s+1}{(s+1)^2+2^2}$
$\frac{s+1}{(s+1)^2+4}$
$\frac{s+1}{s^2+1+2s+4}$
$\frac{s+1}{s^2+2s+5}$ (Ans)