a) Find the Laplace transform of the following expression by using transform tables. f (t) = t³ + sin 2t b) Find the inverse Laplace transform of the following expression by using transform tables. F(s) = + s+5 s²+25 c) Use the First Shift Theory to find the Laplace transform of the following expression. e-3t sinh 5t d) Use Laplace transforms to find the final value of the following expression. f(t) = e-3t sin 4t e) Use the Multiply by t rule to find the Laplace transform of the following expression. f(t) = t²e5t

Q: 3. Find the Fourier transform of of 1/(1+t²).

A: Let  g(t)=e-at Then g^f=∫-∞∞e-ate-2πiftdt      =∫-∞0e-ate-2πiftdt + ∫0∞e-ate-2πiftdt…

Q: (2s-8.4) find the inverse transform of s2+0.4s–0.21 -

A:

Q: Find the Laplace transform of the following: 1. f(t)= (14t)-3e-7t cos(8t) - (2t-6)²

A: Here given function ft=14t92-3e-7tcos8t-2t-62orft=14t92-3e-7tcos8t-4t2-36+24t Use the basic property…

Q: 1. Find the Laplace transforms of (a) t°sinat (b)te" sin3t (c) cosat – cos bt (d) +tsinat t 1-cost…

A: According to our guidelines we can answer only three sub-parts and rest can be reposted.

Q: Find the Fourier Cosine Transform of the function ƒ(x) = (ae-4x + be−³x + ce-²x)² if x>0 if a = 2, b…

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Q: Solve the inverse Laplace transform: 2s-4 s2+8s+13

A:

Q: Jsing the z-transformation table, find the Z transform of the following: (a) {sin} (c) {sinh 2n} (b)…

A: Z transform using table

Q: Find sine transform of e-[165]t/t

A: The Fourier sine transform is defined as                                  Fsfx = Fss = ∫0∞fx sinsx…

Q: 2 f(x) = (ae-4x + be-3x + ce-2x)ʻ if x>0

A:

Q: 2s – 10 -5s

A: We have to solve given problems:

Q: of the function. 4. Find the Fourier transform of of 1/(1+t²).

A:

Q: date Find laplace transform of if 7. Cos (3¢) if t 7 I

A: Solution: Given function is   f(t)=0                      ,   if   t<π4cos(3t)           ,   if…

Q: Use the accompanying tables of Laplace transforms and properties of Laplace transforms to find the…

A: Use the following L{eatcosbt}=b(b-a)2+b2L{eat}=1b-aL{1}=1b

Q: Use the accompanying tables of Laplace transforms and properties of Laplace transforms to find the…

A:

Q: Use the Laplace transform table and the linearity of the Laplace transform to determine the…

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Q: (e-4t – e-t) - e-t) 2t

A: Find the Laplace transform of the function ft=-52t(e-4t-e-t).