Apply the properties of Laplace transform including the linearity property, shifting property, and property of differentiation. 2 a) L(6) and L(5- 2e-) Ans: und- s+1

Q: Find the Laplace transform L(2te3t cos 4t + u(t – 1/2) sin 2t)

A: Here we apply formulas of lapses transformation.

Q: sform of s+2 s° (s+1)(=

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Q: 8. с. (s-4)3

A: Use standard results of inverse Laplace transform to solve this problem.

Q: Evaluate: L-1 [2s-9) ls²+2)

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Q: y = e√√²t sin√√2t √2 (s-√2)² + √2 A) √2 (s -√2)² + 2 √2 (s + 2)² + 2 B) 2 (s-√2)² + 2 9

A:

Q: x2 , Ix1 a = find Fourier transform of f(x)=

A: To determine: The Fourier transformation of  f(x) = x2 ,     x<a 0 ,       x>a

Q: Find the inverse Laplace transform of a (1+ s2 + a2 Cs le

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Q: 1 S F(s) = 2s 2s2 + 56

A: We apply inverse Laplace transform to the given equation and find the function f(t).

Q: 21 (s+ √2) L¹ {- 4)

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Q: 24s? + 128 (s2 – 16)3

A: I have solved using partial fraction

Q: Determine L-1. 2s² +10s (2s²-20s+58) (s+1)

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Q: use convoluHon Lapiace transform 15. to find Inverce (1+zs) =S

A: Let ft & gt be functions with Laplace transforms Fs & Gs respectively that is Lft=FS &…

Q: FindiL [+ sin 5+] IDS a1) s (s*+25) C. S?-25 di) (5?+ 25)2

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Q: unctions f and g have Fourier transforms F[f] – and F[9] = That is the Fourier transform of, h(t) =…

A: Given: Ff=1w2+1Fg=e-w2 A Fourier transform is a mathematical transform that decomposes functions…

Q: 1 F(@) =: 2 - w?+j3w

A: It is known that .  Use the formula below to compute the inverse Fourier transform.

Q: 53+45?+ 35 +452. is

A: Please check step 2 and 3 for solution

Q: The Laplace transform of L(sin 5t sin 4t) is S s2 +12 s+ 92 S 2 [ s2 + 12 s2 + 92 s2 - 12 s2 + 92 s2…

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Q: The Laplace transformLe2t cos cos (4t) C ||

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Q: transform Find the Laplace [(+-1)u(t-1)-[(+-1) (+-2) U

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Q: a) 2-3u(t-5) cost = -t Find the 33 Ordine Lap of

A: The given function is ht=-t cos5t-3ut-5cost To find: the Laplace transform of the given function.

Q: Find L. T. for each of the following functions: (t-4)²u(t-4), (t-3)e-2(t-3) sin 4(t-3)u(t-3).

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Q: Laplace Inverse Transform of 1 (5+1) (5+2) (5²+25+10)

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Q: L[(3e2t)2]

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Q: 3s – 137 L(f) s2 + 2s + 401

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Q: b) Find the inverse Laplace transform of the following function by using convolution theorem 45s…

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Q: { x2, Ix1 a ||

A: Given function is f(x)=x2     x<a0      x>a let the Fourier transform of f(x) is F(s) So we…

Q: TL (s+ π)²· 2 L-¹ {

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Q: S13

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Q: Laplace transform THI f(t) = 3 sint cost

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Q: 1- cos t Find the Laplace transform of

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Q: erform the Laplace Transform Show your Solution 2e-5t sin 10t + 6e-5t cos 10t

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Q: 1 t3e0.035t 2

A: Use the following formulae, to obtain the solution. Laft=aLftLtkft=-1kdkdskLftLeat=1s-addxxn=nxn-1…

Q: Find the Laplace Transform of tet sin (24)

A:

Q: Find L ^ { 4s (s² +9)² by using the convolution theorem.

A: Sol

Q: y = 3sinh (3t) 3 s² +9 A) 6 s² +9 3 S² - 9 6 S²-9

A: Given function is y= 3sinh(3t)