Laplace Transform Technics 13. Find the Laplace transform of x(t), L[x(t)]. 2(t)+3(t)+x(t) = 5, x(0) = 2, ȧ(0) = -1 s'X-5%- x. } +3 {58-x} + & 2s+7 28278 (A) (D) 282 +381 282 +381 (25²+35+ 1) = 2827s+5 (B) s(28² + 38+1) ((E). 482 +48 +5 s(2s2+38+1) 281 (C) -82+5 28238 +1 (F) s(282 +381) 14. Find the inverse Laplace transform of the fol- lowing function. 382+2 X(s) = 83+82 +48 +4 X = 5/3 ון = = 5/5 +25% +2% +370 45-2 +6 45²+45 +5 S 45²+45+5 5(25435+1) (A)e-t +2 cos(2t) sin(2t)
Laplace Transform Technics 13. Find the Laplace transform of x(t), L[x(t)]. 2(t)+3(t)+x(t) = 5, x(0) = 2, ȧ(0) = -1 s'X-5%- x. } +3 {58-x} + & 2s+7 28278 (A) (D) 282 +381 282 +381 (25²+35+ 1) = 2827s+5 (B) s(28² + 38+1) ((E). 482 +48 +5 s(2s2+38+1) 281 (C) -82+5 28238 +1 (F) s(282 +381) 14. Find the inverse Laplace transform of the fol- lowing function. 382+2 X(s) = 83+82 +48 +4 X = 5/3 ון = = 5/5 +25% +2% +370 45-2 +6 45²+45 +5 S 45²+45+5 5(25435+1) (A)e-t +2 cos(2t) sin(2t)
Question
please explain this in depth question 13 only and there is work done on the right but i dont really understand it. why on the right hand side does 5 turn into 5/s what makees that happen. just one specific question i hope u can explain along with the rest of the problem
![Laplace Transform Technics
13. Find the Laplace transform of x(t), L[x(t)].
2(t)+3x(t)+x(t) = 5, x(0) = 2, x(0) =
==
2s+7
(A)
2s² + 38 +1
(D)
28278
2s238 +1
2s²+7s+5
4s² +48 +5
(B)
s(2s2+381)
((E)
s(2s² + 3s+1)
2s+1
(C)
-s²+5
2s2+381
(F)
s(2s² +381)
-1
14. Find the inverse Laplace transform of the fol-
lowing function.
X(s) =
3s2+2
(A)e-t +2 cos(2t) - sin(2t)
$3 + s² +48 +4
2 { s² - ≤ x - x. } + 3 { ≤8-x}
2{5'8-
+ x =
5/5
(25²+35+ 1) = 5+25x+2%
P
✗=
ון
ין
=
5/3
+
+3%
45-2 +6
45²+45+5
S
45²+45+5
5(25435+1)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fadcd2146-40e8-4924-8383-3d1cdc877b03%2F9b560557-d111-42c7-89d2-217e28ff604a%2Frk1fi1d_processed.png&w=3840&q=75)
Transcribed Image Text:Laplace Transform Technics
13. Find the Laplace transform of x(t), L[x(t)].
2(t)+3x(t)+x(t) = 5, x(0) = 2, x(0) =
==
2s+7
(A)
2s² + 38 +1
(D)
28278
2s238 +1
2s²+7s+5
4s² +48 +5
(B)
s(2s2+381)
((E)
s(2s² + 3s+1)
2s+1
(C)
-s²+5
2s2+381
(F)
s(2s² +381)
-1
14. Find the inverse Laplace transform of the fol-
lowing function.
X(s) =
3s2+2
(A)e-t +2 cos(2t) - sin(2t)
$3 + s² +48 +4
2 { s² - ≤ x - x. } + 3 { ≤8-x}
2{5'8-
+ x =
5/5
(25²+35+ 1) = 5+25x+2%
P
✗=
ון
ין
=
5/3
+
+3%
45-2 +6
45²+45+5
S
45²+45+5
5(25435+1)
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