3s 14 82-4s +8 - 3e cos 2t + 4e2" sin2t 3et cos 2t –4e2" sin2t - Option 1 O Option 2 4e2t cos 2t + 3et sin2t 4e-2t cos 2t +3e 4 sin2t -2t O Option 3 O Option 4

Q: 4s+ 12 82 + 8s + 10 4e" - 4te" 4e-4 - 4te 4 Option 1 Option 3 4e + 4te Option 4 O None of the…

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Q: Use Theorem 7.1.1 to find (f(t)). (Write your answer as a function of s.) f(t) = 4t² - 2 sin(3t)…

A: Laplace transform is used to find the solution of the differential equation. Laplace transform is…

Q: Find the following inverse laplace For simplification, you can use x = 22

A: Given that,Fs=xssx-s-xThe given value of x is 2Substituting x=2 in the given function, we…

Q: 6s L-1 (s² + 9)²

A: Apply the inverse transform rule that is if L-1Fs=ft  then L-1sFs=ddtft+f0  . The expression 6ss2+92…

Q: 12s+48 7. F(s) = s2 +8s+16

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: Find the inverse Laplace of the following Note: Factor, Reduce to Simplify before getting the…

A: Given that, F(s)=s2+3ss4+5s3+7s2+5s+6 Factoring, we get,…

Q: Pinverse aplace in of S 25²-1 1 (5² +49) ²

A: We have to find the inverse Laplace transform of the functions s2s2-1 and 1s2+492.

Q: s-1 s(s+ 1)² -1+et+2te-t 2+te-t-e-t O Option 1 Option 3 1+et-2te-t Option 2 -2+tet + et O Option 4

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Q: Evaluate t=0.01, Given: 21' + 20I = 100sin(150t) Round-off to 3 decimal places.

A: Given differential equation is2I'+20I=100sin150tI is evaluated at t=0.01 as shown below.

Q: (s) = 20 (s+3)(s² +8s+25) f(t)=2e-3t2e-4t cos3t- -

A: As per the guidelines I am answering only one question at a time.[1]

Q: 23. F(s) = 5s² + 34s + 53 (s+3)²(s+1)

A: We will partial fraction decomposition to separate the factors of denominator and then use inverse…

Q: 1 1. s2 + 2s + 10

A: The solution is given as

Q: f(1) = sin? (t + x) sin (t + ) = S1

A: Given:      ft=sin2t+π

Q: -1 Find a) S-4 4(S-3) +16 1 -- b) 8 e StI

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Q: L-1 2 l(s + 3)(s + 5) 5)] -

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Q: Solve for the Inverse Laplace of this equation

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Q: d²x 2. dt dx dx 2- + 3x = 0 x(0) = 1, (0) = 0 - dt2 dt

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Q: s+1 (a)x= ¹ {= 1/12) b)x=² { = s²-4s Q1) Find: a)¯¹) 3s + 1 s²-4s+1)

A: We know  and

Q: 3s +2 1 Find L-1 s2 + 4s + 29

A: To find laplace inverse.

Q: s+ 8 F(s) %3D s2 + 16s + 68

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Q: 7s? – 41s + 84 (s – 1)(s² – 4s + 13) F(s)

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Q: f(S) 7 (S+2) (S+2)(s2-4S+20) QI/ A)Find the inverse of elue

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Q: s+9 s + 1)(s² + s + 1)

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Q: Find the inverse Laplace of the following functions: 3s2 +s+3 F(s) = (s²+1)(S+1)(s²+4) i. %3D

A: Hello. Since you have posted multiple questions and not specified which question needs to be solved,…

Q: d²x dx dx -(1) = 2 4- + 4x = 0 x(1) = 0, - dt2 dt

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Q: 1) S-4 5²-85+ 10

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Q: d) L{e f, sin dr}

A: