Consider a causal LTI system characterized by differential equation dytdt-4yt-2xtThe steady state output yt is A sin 4t- for the input ej4t-e-j4tj then the value of A is - Answer upto two decimal places

Given system is, dy(t)dt+4y(t) = 2x(t) (s+4) Y(s) = 2X(s) ∴ nbsp; H(s) = Y(s)X(s) = 2s+4 e^j4t e^ j4tj = 2 sin 4t y(t) = 2 [ 2j4+4 ]sin [ 4t tan 1 ( 44 ...

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Standard XII

Physics

v-t Graph

Consider a ca...

Question

$Consider a causal LTI system characterized by differential equation \frac{d y (t)}{d t} + 4 y (t) = 2 x (t)$

$The steady state output y(t) is A sin (4 t + Φ) for the input \frac{e^{j 4 t} - e^{- j 4 t}}{j} then the value of A is ___.$ $(Answer upto two decimal places)$

0.71

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Solution

The correct option is A 0.71
Given system is,

$\frac{d y (t)}{d t} + 4 y (t) = 2 x (t)$

$(s + 4) Y (s) = 2 X (s)$

$∴ H (s) = \frac{Y (s)}{X (s)} = \frac{2}{s + 4}$

$\frac{e^{j 4 t} - e^{- j 4 t}}{j} = 2 s i n 4 t$

$y (t) = 2 [\frac{2}{j 4 + 4}] s i n [4 t - t a n - 1 (\frac{4}{4})]$

$y (t) = \frac{1}{\sqrt{2}} s i n [4 t - 45^{o}]$

$∴ A = \frac{1}{\sqrt{2}} = 0.707$

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Consider a causal LTI system characterized by differential equation dy(t)dt+4y(t)=2x(t) The steady state output y(t) is A sin (4t+Φ) for the input ej4t−e−j4tj then the value of A is ___. (Answer upto two decimal places) 0.71

The correct option is A 0.71Given system is, dy(t)dt+4y(t)=2x(t) (s+4) Y(s)=2X(s) ∴H(s)=Y(s)X(s)=2s+4 ej4t−e−j4tj=2sin4t y(t)=2[2j4+4]sin[4t−tan−1(44)] y(t)=1√2sin[4t−45o] ∴A=1√2=0.707

$Consider a causal LTI system characterized by differential equation \frac{d y (t)}{d t} + 4 y (t) = 2 x (t)$

$The steady state output y(t) is A sin (4 t + Φ) for the input \frac{e^{j 4 t} - e^{- j 4 t}}{j} then the value of A is ___.$ $(Answer upto two decimal places)$

0.71