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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