GATE Electrical Engineering (EE) 2020 Solved Paper

Question : 19 of 65

Marks: +1, -0

Consider a linear time-invariant system whose input

r(t)

and output

y(t)

are related by the following differential equation:

\;{d^{2} y(t)}/{d t^{2}}+4 y(t)=6 r(t)

The poles of this system are at

Solution:

\;{d^{2} y(t)}/{d t^{2}}+4 y(t)=6 r(t)

r(t)

is Input

{y}( {t})

is output
Taking Laplace transform both sides

s^{2} y(s)+4 y(s)=6 R(s)

T(s)=\;{Y(s)}/{R(s)}=\;{6}/{(s^{2}+4)}

For calculation of poles,

{s}^{2}+4=0

{s}=± {j} 2

Poles of this system are

+2 j,-2 j

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