Problem One а) Find Laplace transform of f(t) = te-tcost (Hint:L[t" ƒ(t)] = (-1)"F(") (s)) 3s-7 b) Find Inverse Laplace transform of F(s) : s2+2s+5' sta (Hint:L[e¬at cosbt] L[e-atsinbt] = %3D (s+a)²+b²' (s+a)²+b²'

Q: 4s = s²-2s+5 _F(s) =

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Q: QI\ Find Fourier transform for: A) f(t) = U(t)sin² (3t) C) f(t) = elct sinh(bt)

A: (A)Given the function f(t)=u(t)sin2⁡(3t).Rewriting, .We know that, .The Fourier transform of f(t) is…

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A: Step 1: Step 2: Step 3: Step 4:

Q: Find the inverse Laplace transform f(t) = £¯¹ {F(s)} of the function F(s) = e −3s (1 – 4s) s² + 16

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Q: 2. ts) Use the table of Laplace Transforms and 1st shifting theorem to find the Laplace transform of…

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Q: Part A how that L(tnf(t)) = (−1)n ((dnF(s))/(dsn)), where F(s) is the laplace transform of y(t). In…

A: Hi, It is multiple sub-parts, I am going to solve the first part only.

Q: 2. (a) Find the Laplace transform of the function f(t)=4e¹-4te-2 +21²e-3t 0 (b) Find the Laplace…

A: Part a and b asked and answered.

Q: Question 2: Calculate the inverse Laplace transform of the function F(s) = (s + 1)/(s^2 + 4s + 5).

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Q: Part A) How that L(tnf(t)) = (−1)n ((dnF(s))/(dsn)), where F(s) is the laplace transform of y(t). In…

A: The problem is related with Laplace transform.  First in part (A), we have to show that Ltnyt =…

Q: Y(s) = %3D

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Q: The inverse Laplace transform of F(s) = = -98 e 8² +18 2 is

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Q: s+4 (d) s' + 2s + 5

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Q: Find the inverse Laplace transform L{F(s)} of the given function. 8s2 – 24s + 72 F(s) = s(s² + 36)…

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