Find inverse laplace find y(t) for the following Y(s)=8s+1s−3⋅e−2s

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Khaleesi Herbert

Answered question

2020-11-30

Find inverse laplace
find y(t) for the following
$Y (s) = \frac{8}{s} + \frac{1}{s - 3} \cdot e^{- 2 s}$

Answer & Explanation

pattererX

Skilled2020-12-01Added 95 answers

Step 1
Consider the given function,
$Y (s) = \frac{8}{s} + e^{- 2 s} \cdot \frac{1}{s - 3}$
use the inverse transform rule which states that,
$if L^{- 1} {Y (s)} = f (t) then L^{- 1} {e^{- a s} Y (s)} = U (t - a) f (t - a)$
$L^{- 1} {\frac{1}{s}} = 1$
$L^{- 1} {\frac{1}{s - a}} = e^{- a t}$
Step 2
by using the above rules the inverse Laplace transform of the function will be,
$L^{- 1} {Y (s)} = L^{- 1} {\frac{8}{s} + e^{- 2 s} \frac{1}{s - 3}}$
$f (t) = L^{- 1} {\frac{8}{s}} + L^{- 1} {e^{- 2 s} \frac{1}{s - 3}}$
$= 8 + U (t - 2) L^{- 1} {\frac{1}{s - 3}} (t - 2)$
$= 8 + U (t - 2) e^{2 (t - 2)}$
hence the inverse Laplace transform is $f (t) = 8 + U (t - 2) e^{2 (t - 2)}$

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