The inverse laplace transform of signalXs -4s-2s-4- if ROC is -2 - Res - -4 is

X(s) =4(s+2)(s+4)=As+2+Bs+4 A = 2 and B = 2 X(s) =2s+2 2s+4 Since given ROC is, 2 gt; Re(s) gt; 4 The term with pole = 2 will be left sided sign ...

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Standard VIII

Physics

Luminous Intensity

The inverse l...

Question

The inverse laplace transform of signal $X (s) = \frac{4}{(s + 2) (s + 4)}; i f R O C i s - 2 > R e (s) > - 4$ is

- 2 e^{- 2 t} u (- t) - 2 e^{- 4 t} u (t)

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2 e^{- 2 t} u (t) - e^{- 4 t} u (- t)

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2 [e^{- 4 t} - e^{- 2 t}] u (- t)

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2 [e^{- 2 t} - e^{- 4 t}] u (t)

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Solution

The correct option is A $- 2 e^{- 2 t} u (- t) - 2 e^{- 4 t} u (t)$
$X (s) = \frac{4}{(s + 2) (s + 4)} = \frac{A}{s + 2} + \frac{B}{s + 4}$

$A = 2 a n d B = - 2$

$X (s) = \frac{2}{s + 2} - \frac{2}{s + 4}$

Since given $R O C i s, - 2 > R e (s) > - 4$

The term with pole = -2 will be left sided signal and pole = -4 will be right sided signal
$∴ x (t) = - 2 e^{- 2 t} u (- t) - 2 e^{- 4 t} u (t)$

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The inverse laplace transform of signalX(s)=4(s+2)(s+4); if ROC is−2> Re(s)>−4 is

The correct option is A −2e−2tu(−t)−2e−4t u(t)X(s)=4(s+2)(s+4)=As+2+Bs+4 A=2 and B=−2 X(s)=2s+2−2s+4 Since given ROC is,−2>Re(s)>−4 The term with pole = -2 will be left sided signal and pole = -4 will be right sided signal ∴ x(t)=−2e−2t u(−t)−2e−4t u(t)

The inverse laplace transform of signal $X (s) = \frac{4}{(s + 2) (s + 4)}; i f R O C i s - 2 > R e (s) > - 4$ is