Compute the inverse Laplace tranform of (a) G(s) = = 18 54-9 S (b) F(s) = 3² +45 +40

Q: F (s) = e4-3s (s+4)5/2

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Q: Apply Laplace Transformation for the “function of sinh(at).”

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Q: f(d) = e-2d d4

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Q: + dy-39 sin ax y co) y'o) =12

A: Laplace transferom for the differential equation

Q: t3 - 3t2 + 5t – 8

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Q: 3(s-4)e-5s F(s): %3D s2-8s+25

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Q: 3s2 + 5s + 1 (s)= (s2 + 15s + 34) %3D

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Q: f(t) = 6te-3t + te-5t sin5t + t² %|

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Q: Find inverse Laplace by residue theory 2. XeS+(て-2x。) s- 25+5

A: Find the Laplace inverse transform by residue theory L-1x0s+x1-2x0s2-2s+5

Q: Use the transforms in the table below to find the inverse Laplace trans form of the following…

A: By using given table we will find the Laplace inverse transformation.

Q: 5 sinh (3t) +4 cosh (3t)

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Q: Which of the following pair of functions is linearly independent? (a) e, e(*-3) (b) 4, sin2x+ cos2x…

A: Which of the following pair of functions is linearly independent?

Q: Let (t) , a) Find the domain of F(t) b) Find " (t)

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Q: 3) Find the function of y = 1) Reflect about the (2) Shift up (3) Shift X-axis 8 Units left 7units

A: The given function is y=x1) Reflect about x-axis2) shift up 8 units3) shift left 7 units

Q: Explain the geometric meaning of r'(t).

A: Let the function is given as ,  rt=ft, gt, ht The derivative of the function is, r't=f't, g't, h't…

Q: Solve the Laplace transform of: 3 cos 8t + 2 sin 8t

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Q: Find the Laplace Transformations of the following functions i. L{(sin t + cost)² - cos² 3t}…

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Q: 1) S-4 5²-85+ 10

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Q: Show that the function u = In(X² + Y2) is harmonic and find the conjugate harmonic v.

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Q: ₂ (91+₂²) - F(S)

A: Given: Fs=1s2+162. We have to find the inverse Laplace using convolution.

Q: I- 100 (s+10) (s+20)

A: Inverse Laplace transform

Q: Find derivatives of the A) (2x-5)3

A: Since you have asked multiple questions in single request  so we  will be answering only first…