(c) Translate the pulse, i.e. move the nonzero value of the func- tion to a different location while maintaining the width [for example, let f(t) = 1 for 1 ≤ t ≤ 2 and zero elsewhere; then try for f(t) = 1 for 2 ≤ t ≤ 3 and zero elsewhere; and so on.] Show that it obeys the translation property of Laplace Transforms, L{f(ta)} = e-as F (s). (d) Widen the pulse, i.e. keep the other eage at zero and in- crease the width of the nonzero value [for example, extend to f(t) = 1 for 0 ≤ t ≤ 2 and zero elsewhere; the do for f(t) = 1 for 0 ≤ t ≤ 3 and zero elsewhere]. Show that you can get the scaling property of the Laplace Transform, L {f(at)} = F (₁).

Q: ∞ -3t Evaluate test sin 3t dt. [Hint: Use the definition of Laplace transform]

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Q: Determine the Laplace transform of f(t) = 5sin 2t - 6t * cos 2t

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Q: Determine the Laplace transform of f(t) = tcosh(t)

A: To Determine:  Laplace transform of f ( t ) = t cosh( t)

Q: a) Find the Fourier transform of 4 f(t) = e tu(t) + -tu(t) + ²9.

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Q: Compute the Laplace Transform of f(t) e-St using the definition of the transform. (Just listing the…

A: ANSWER:

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

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Q: Find the Laplace transforms of the following function: g(t) = 7e-#(6t – e*)².

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Q: 32-P(t):l0+8t. 33. f(t): expl-5t] +4t" 34-f(t): : et [coslut) +6]

A: Thanks for the question :)And your upvote will be really appreciable ;)

Q: 2. Calculate the inverse Laplace transform: 2s (a) C- C-¹ { 25+32 }; (b) C-¹ ( 25-3₂} 2s L-1

A: We have to find the Laplace inverse transformation of and

Q: Use the definition of Laplace transform only (no tables) to find Laplace transform of f(t)=4te7t

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

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Q: L{ sin2(t-1) cos3rdt}

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Q: Let x(t)=5sinc(1.5t) +6cos(7/2) and h(t)=4sind(). Determine y(t)=x(t)*h(t) using Fourier Transform…

A: Let  and We need to determine y(t)=x(t)∗h(t).To solve this problem, we list the Fourier transforms…

Q: f (t) = eat+b

A: The solution is given below:

Q: Determine the Laplace Transform of est cos 5t .

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Q: 3) Find Fourier Transform for the following function as in figure: vsing this FLw)-ズ fit) fcx) e iwy

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Q: Compute the Fourier transform of the following function: f (x, y) = e-(1x-y|+|x+y[)<+

A: Calculate Fourier transform: Fu,v=∫y=-∞∞∫x=-∞∞fx,ye-2πjux+vydxdy…

Q: find the Laplace transform of t²cos(wt)

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Q: d.-tte-6c 3

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Q: Use Eq. 3-1 to show that the Laplace transform of (a) ebt sin wt is b) ebt kos wt is W (s+b)² +w² W…

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Q: Find Fourier transform for : A) f(t) = e-3t cos² (3t) B) f(t) = te tu(t - 3)

A: (A)Given f(t)=e−3tcos2⁡(3t).Now, we'll find the Fourier transforms for individual terms.The Fourier…

Q: Determine an inverse Laplace transform of the function. [2] a) 4s b) 2/54 +

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Q: Q1. a) Derive the Laplace transform of 3e4t from first principles (i.e. without using the list of…

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Q: Let f(t)= for 0<t<1 for t≥1 a. Find L{f(t)} by using the definition of Laplace transformation. b.…

A: Let's find.

Q: Find the Laplace transform using convolution theorem: Te2" sin(2(t - T))dr.

A: So, here f(t) = sin(2t) and g(t) = t e2t.

Q: Find the laplace transform of the following: a.) f(t) = teatcosb

A: # as per the guidelines we are entitled to solve one question at a time, please resubmit the other…

Q: Calculate the Laplace transform L{f} of the function f(t) = et+2 8t° + 8 sin(2t) + 9 using the basic…

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Q: Q1) a) Find L[ (k - ht)².t²] RI Find the Laplace transform of: f (t)= et, cos² (3t)

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Q: I the Fourier transform of f(t)= 3sin5t +4cosl %3D

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Q: Find the Fourier transform of f(t) = [Aeat ]u(t) %3D and draw the amplitude and phase spectrum

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Q: Inverse Laplace transfor a. etsin4t b. 1/2etsin4t

A: This is a problem of Laplace transform.