GATE Electronics and Communications (EC) 2020 Solved Papers

Question : 58 of 65

Marks: +1, -0

A system with transfer function

{G}( {s})=\;{1}/{( {s}+1)( {s}+ {a})}, {a}>0

is subjected to an input

5 {cos}

3t. The steady state output of the system is

\;{1}/{√{10}} \cos (3 t-1.892) .

The value of a is ____________

Solution:

\;\text " Where "\; {M}=| {G}(j ω)|_{ω=ω_{0}}

{G}( {j} ω)=\;{1}/{(1+ {j} ω)+( {a}+ {j} ω)}

| {G}( {j} ω)|=\;{1}/{√{(ω^{2}+1)(ω^{2}+ {a}^{2})}}

{M}=| {G}( {j} ω)|_{ {l}=3}=\;{1}/{√{(10)( {a}^{2}+9)}}

{AM}=\;{1}/{√{10}}=\;{5}/{√{10} √{ {a}^{2}+9}}

{a}^{2}+9=25

{a}^{2}=16

{a}=4

∵ {a}>0

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