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

Correct Answer is : u(t)−2e−tu(t)+e−3tu(t)

2 {u}( {t})-2 {e}^{- {t}} {u}( {t})+ {e}^{-3 {t}} {u}( {t})

GATE Electronics and Communications (EC) 2019 Solved Paper

Question : 20 of 65

Marks: +1, -0

Let

{Y}( {s})

be the unit-step response of

{a}

causal system having a transfer function

G(s)=\;{3-s}/{(s+1)(s+3)}

that is,

Y(s)=\;{G(s)}/{s} .

The forced response of the system is

Solution:

{y}( {s})

is unit step response

∴ {y}( {s})= {G}( {s}) × \;{1}/{ {s}}

=\;{3- {s}}/{ {s}( {s}+1)( {s}+3)}

=\;{ {A}}/{ {s}}+\;{ {B}}/{ {s}+1}+\;{ {C}}/{ {s}+3}

∴ {y}( {s})=\;{1}/{ {s}}-\;{2}/{ {s}+1}+\;{1}/{ {s}+3}

∴ {y}( {t})= {u}( {t})-2 {e}^{- {t}} {u}( {t})+ {e}^{-3 {t}} {u}( {t})

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