Gate 2016 EE (Set 1) Q6

6. The transfer function of a system is  Y(s)/R(s) = s/(s+2) The steady state output y(t) is A(2t+\phi ) for the input cos(2t). The values of A and \phi , respectively are:----------

Solution:

Formula,H(\omega )=\omega /\sqrt{}(\omega^2+a^2 ) ; \phi =90-tan^(-1)?(\omega /a)

a=2;H(\omega )=\omega /\sqrt{}(\omega ^2+4);\phi =90-tan^(-1)?(\omega /2)

When \omega =2,H(2)=1/\sqrt{}2 and \phi =90-tan^(-1)?(2/2)=90-45=45^{0}

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