Using the laplace transformation table, evaluate the following, considering any other variable other than t as constant: L[(at − b)^2 sin bt]

Q: Find the Laplace transform of the function

A: The Laplace transform of the function is represented as or , it is defined as , since the…

Q: (d) f"(t) - 4f (t) = sin 2t where f(0) = 1 and f'(0) = -2

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Q: 1 F(s) = s(s² +2s + 2)

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

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Q: 1-1 at (1s) moves aloing C be A ball Starts Curve at (o,1), Let find the parametetization EA7 the…

A: Please check step 2 for the solution.

Q: (ii): f(t) = sin (t + 7)+ e³' cosh 5t

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Q: 7) f(x)= xe-x 0 if -1<x<0 otherwise

A: Formula for the Fourier Transform of fx is  Fw=∫-∞∞fxeiwxdx  We are given fx=xe-xif…

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: contour

A: For first Contour we use Cauchy Residue Theorem and for second we use Cauchy Integral Formula.

Q: 2. x(t) = e5t + cos 3t %3D

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Q: e at -e bt

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Q: Find the Laplace transform

A: Given,

Q: (t – 1)* 24 24 12 4 1 24 24 12 4. O option 2 Option 1 24 - 24s- 12s2+ 4s° + s4 24 - 24s +12s2- 4s +…

A: Using Laplace Transform to Evaluate the Function (t-1)^4

Q: 3. x(t) = 3t7 + 8

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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: Sketch the following functions and find their Laplace Transforms: 3.) sinwt (0 < t < =)

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Q: 1. x(t) = 3t5

A: Given Function: x(t)=3t5 constant multiplication property of Laplace Transform:…

Q: b) 4 (€) -et cos (dt+물) cos (2dt +물) COS 3

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Q: g(t)= 2e"u(t – 1) p(t) = 6[u(t – 2)– u(t –4)]

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