5- Which of the following is the inverse Laplace transform of the function X (s) = s+ 4s +8 -2t cost -e sin 2t b) cost 'sint 6- The Laplace transform of the (e" sin 3t) is 3 3 2 a) (s – 2)? +9 b) (s +2)? +9 (s - 2)2 +9

Q: 3.15 - Find the inverser Laplace transform of the following functions: 5e-2s d. G(s) = (s+1)(s²+s+1)

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Q: -4 Inverse Laplace transform of is given by s2-16 sinh(-4t) O sinh(4t) O cosh(4t) O cos(-4t)

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Q: 8 The inverse Laplace transform of the function is sin(3t) (A) t – 3 sinh(3t) (B) t- 3 sin(3t) (C)…

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Q: 1. In cases of Laplace transform, specify the region of convergence. Compute the Laplace transform…

A: f(t) = sinπt2  ; 0 ≤ t ≤ 5Laplace transform needs to be found... We know that, Lsin(at) = as2+a2Now,…

Q: Q1\ Find the Z-transform of A) cosh 2

A: The given question can be solved as shown in step2.

Q: kado/4 Find the Laplace transform for -4 f() = e'sin2t + e cost s + 1 2 s+1 s + 2s + 5 s- 2s + 2 (s-…

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Q: 3s +5 Let X(s) = be the Laplace Transform of a signal x(t). Then, x(0+) is %3D s + 10s + 21

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Q: SOLVE FOR INVERSE LAPLACE TRANSFORM 6s – 4 - s2 4s + 20

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Q: 13. ) Find the Laplace transform of a) f) = 3e-t + 2 cos(t) – 5t3/2

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Q: -4 Inverse Laplace transform of is given by s2+16 O sinh(4t) O cosh(4t) O cos(-4t) O sin(-4t)

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Q: 8.(a) Find the Fourier transform for the function cos x, -n/2 7/2 f(x) = 0, (b) Use the result in…

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Q: Find the inverse Laplace transform of -6s e F(s) = s2 + 2s – 3 - - (Use for u.(t) .)

A: The given expression is Fs=e-6ss2+2s-3. We have to find the inverse Laplace transform of function…

Q: 2) There is a function F (s) with "different true root state". Make the inverse laplace transform of…

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Q: 7. Given that the Laplace transform of te is F(s) =- (s + k) Laplace transform of te" without using…

A: The solution is given as

Q: 8. Find the function whose Fourier sine transform is the following function. S[u] - 2 0 x = [1, 2],…

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Q: The Laplace transform of L2 sin 6t sin 3t] is S - s + (3)² s2 + (9)2 S 2s + (9)* s2 + (9)² s² + (3)²…

A: Solution by using trigonometric identities and Laplace transform table as follows :

Q: FIND THE LAPLACE TRANSFORM OF THE FOLLOWING USING TABLES OF LAPLACE TRANSFORM AND ITS PROPERTIES.…

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Q: FIND THE LAPLACE TRANSFORM OF THE FOLLOWING USING TABLES OF LAPLACE TRANSFORM AND ITS PROPERTIES.…

A: The solution is given as

Q: Solve for the Laplace transform of e2t sint cost cos 2t cos 4t 1 s-4s+20 s-4s+68 -4s+20

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Q: 5. Use Laplace transform technique to solve , y"-y'-6y = 0, Given y(0) =1 and y'(0) = -1

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Q: 8 3 Find the Inverse Laplace Transform of- + 3s2+ 12 s2– 49 3 4 A) - sin2t + -cosh ( 7t) 7 3 4 –…

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Q: 27 (- 1 -' -p = 1, 2, 3, ... p . Find f (x) if its finite sine transform is given by f.(P). where 0…

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Q: (1, |x| 15 Q.1 Find the Fourier transform of f (x) defined by f (x) = %3D Hence evaluate S: sins…

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Q: Consider the IVP: y" - y' + 2y = 8sin(2t) - 8, with y(0) = -2, y'(0) = -4. Solve the IVP by using…

A: Given IVP is y''-y'+2y=8sin2t-8              (i) With y0=-2, y'0=-4 Taking Laplace transformation of…

Q: Solve for the Laplace transform of et sint cost cos 2t cos 4t 7+4s+20 82-4+20 -4+68 4s+8

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Q: 1 Find the inverse Laplace transform of X(s) = given ROC: -1<o<3. (s + 1)(s – 3) x(t) =

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Q: What will be the numerical coefficient of cos(V3t)etin the Inverse Laplace Transform of 3 s(s3-8) O…

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Q: (2) Find Inverse Laplace transform for; 1 1-F(s)= s(s +1) 3 2-F(s)=- s' +4

A: We need to find the inverse Laplace transform. Part(1) We have 1ss+1 We use partial decomposition.…

Q: Find the Fourier transform for S(2)%3D sin a, 2 0.

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Q: 10s – 3 - Find the inverse Laplace transform of F(s) s2 – 4 - 17 O f) 23 -2t -e 4 23 4 17 + 4 -2t…

A: I have stated the used formulas in the solution

Q: What is the value of the inverse Laplace transform given by L 2s+1 8 J s2 +2s +3 O a. e-t (2…

A: Some Laplace inverse transform formulas: L-1(s-a)(s-a)2+b2=eatcosbtL-1b(s-a)2+b2=eatsinbt

Q: 8(a) Using Convolution theorem, find the inverse Laplace transform of s2 +aP

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Q: 3s-2 2s2-4s+2

A: The given function is                                             3s-22s2-4s+2

Q: 5. Determine the Laplace Transform of te2t cos5t s2-2s+11 a. (s²+4s–29)² s2+2s+21 b. (s2+4s+13)2…

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Q: 2.) cos (10t+1)

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Q: The Laplace transform of L[2 sin 5t sin 4t is s+ (1)2 s2 + (9)2. 2s s2 +(1)2 s2 + (9)2 s2 + (1)2 s2…

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Q: Give the Laplace transform of -2x 0Sx and x < 3 f(x) = 4 3<x -3s 27 20 O F(s) = -- b) O F(s) = - -3s…

A: Solution :-

Q: 1- 3s Find the Inverse Laplace Transform of G (s) = s2+ 8s + 21 13 re A 8(1) = - 3e -'cosh(V51) +…

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Q: The Laplace transform of t sin(3t)is : 30s2-54 (s2+9)3 12s-54 (s2+9)% 18s-54 (s2+9)2 12s2-54 (s?+9)?…

A: We find the last transform of t2sin(3t)

Q: 2. Which of the following gives the correct inverse transform of the given F(s)? 8. F (s) = s(s² +…

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Q: By applying inverse Laplace Transform, we get > y(x) = L-1ſ _2s² + 2 Is²(s² + 5). L={ } - L{4 ++}…

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Q: 2. Given the nonlinear sine-Gordon eqn. ua - Sin u, u(t, z), (4 = tig), k: constant (1) Also, given…

A: Given: u(tx)=Sin u, u(t, x),  (u(xt) = u(tx)), k=constant

Q: 1: A :Find Laplace Transform of f(t) = sin²t By Rule.

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Q: 9. Find the mverse laplace transform of system function HS) = for 3 cases of ROCs when- s45s+6 (1)…

A: Consider the given function. Hs=1s2+5s+6 Find the factor of the denominator.…

Q: 7s Inverse Laplace transform of is given by s2-9 O 7 cosh(3t) O 7 sinh(3t) O 7 cos(9t) O 7 cos(-3t)

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Q: 2. Laplace STO 2 3. What is the Laplace transform of 2cos t?

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Q: Find the inverse Laplace transform 01 2 Ou44(1-4) usinh(t — 4) O sinh4(1-4) 0 1 u4cosh4(1-4) 01 4…

A: Given problem:- Find L-1e-4ss2-16