An input of $1 s i n 2 t + 0.3 s i n 20 t$ is applied to a first order insturment having a time constant of $0.2 s e c$ . The output is

0.93 s i n (2 t - {0.23}^{o}) + 0.073 s i n (20 t - 76^{o})

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1 s i n (2 t - {21.8}^{o}) + 0.3 s i n (20 t - {2.3}^{o})

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0.93 s i n (2 t - {21.8}^{o}) + 0.073 s i n (20 t - 76^{o})

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1 s i n (2 t - 23^{o}) + 0.3 s i n (20 t - {2.3}^{o})

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Solution

The correct option is C $0.93 s i n (2 t - {21.8}^{o}) + 0.073 s i n (20 t - 76^{o})$
output to input ratio for first order insturment
$M = \frac{1}{\sqrt{1 + (ω τ^{2})}}$

$x (t) = 1 s i n 2 t + 0.3 s i n 20 t$

$Y (t) = \frac{1}{\sqrt{1 + (ω_{1} τ)^{2}}} s i n (2 t - t a n^{- 1} (2 \times 0.2) + \frac{0.3}{\sqrt{1 + (ω_{2} τ)^{2}}} s i n (20 t - t a n^{- 1} (20 \times 0.2)$

$= \frac{1}{1 + (2 \times 0.2)^{2}} s i n (2 t - {21.8}^{o}) + \frac{0.3}{\sqrt{1 + (20 \times 0.2)^{2}}} s i n (20 t - 76^{o})$

$= 0.93 s i n (2 t - {21.8}^{o}) + 0.073 s i n (20 t - 76^{o})$

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