Let f satisfy f (t +T) = f(t) for all t >0 and for some fixed positive number T; f is said to be a periodic with the period T on 0

Q: A function f (t) = e-at is defined for a > 0 andt > 0. By finding the Fourier transform show that…

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Q: Ex. Find the Laplace transform for the functions 1-f (t) = sin't %3D 2-f (t) =t°e"

A: We have to use Laplace standard transformations.

Q: Q1\ Find the Laplace transform for the following function: f(t) = - 24 t5/2 + t e3t sin (6t)

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Q: Use the definition of the Laplace transform to find L{cos(at)} where a is a constant. You must use…

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Q: Find the Fourier Cosine Transform of the function 0026.png 2 e2.x + be3* f(x)= if x>0 ,6x fb = 10 .…

A: Given function is f(x)=e2x+be3xe6x2 if x>0we have to find the fourier cosin trasformation of this…

Q: f (t) = e(-3t) sin(2t) cos(3t) cosh(t)

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Q: find the Fourier transform f(x) = e ¹² cos fx|

A: What is Fourier Transformation: A mathematical transformation known as the Fourier transform…

Q: Find the Laplace transform F(s) = L{f(t)} of the 3t-18 function defined on the interval J\") 190 U),…

A: (.)  The given function is ,           we find the Laplace transform of the given function .here…

Q: Find the Laplace transform F(s) = C {f(t)} of the function f(t)=et 12u(t-4). defined on the interval…

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Q: L Find the Laplace transform F(s) = {f(t)} of the function f(t) = et-2h(t-2), defined on the…

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Q: Find the inverse Laplace transform L-'{F(s)} of the function e-8s F(s) %3D s2 + 6s – 27 NOTE:…

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Q: Let f(t) = e^t if 0=1   Write f(t) using step function and find the laplace transform. Also,…

A: We have to write f(t) using step function and find the laplace transform. Also, draw the graph.

Q: A. Find the Laplace transform of each given expression (5 (2) i++ t sin(3t) + y, where x = z(t), a…

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Q: Find the Laplace transform of f(t) = cos(2t) * u

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Q: L[t e-t sin 3t dt ]

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Q: Find the inverse Laplace transform f(t) of F(s) = (e-s-e-3s)/(s2

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Q: For f(t) = e-t – 1, find the Laplace transform of t Then, for g(t) = e-t – 2, (9(t) examine if the…

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Q: Find te Inverre laplace transform of F(s) 48 2. |

A: Inverse Laplace Transform Definition: If Fs be the Laplace transform of a function ft, i.e., if…

Q: . Find the Laplace transform of the function f(t) = 2t + 3 cos(3t) + 4 sin(3t)

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Q: Derive the Fourier transform for f(t) = te2t for t>0 and 0 for t<0.

A: The Fourier transform of the function f(t) is represented as F(k), it is defined as ∫-∞∞e-iktf(t)dt,…

Q: Find the Laplace transform of f(t) = sin² 5t a. 50/($³+125s) 25/(s³+ 100s) b. C. 25/(s³ + 125s) d.…

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Q: Find the Fourier Transforms of the indicated function: f (x) = e-3x for x > 0 and f (x) = e2x for x…

A: We have,fx=e-3xx&gt;0e2xx&lt;0 To Do: Find the Fourier Transform of the given function.

Q: If the Fourier transform of f(t) = is F(w), express the Fourier transform of g(t) = 2 0<t<1 0…

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Q: 3 3 e. f(t) 5 sin2t *cos2t e-'cos2t - 10

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Q: How is the existence of the Laplace transform of a function guaranteed?

A: We known that the  Existence of the Laplace transform of a function guaranteed

Q: Q5- Find the Laplace transform, if it exists, of each of the following functions f(t)= {3t²6t+ e-5t}…

A: The given problem is to find the Laplace transform of the given functions.

Q: Q1) Find the Laplace transform of the following functions:- f (t) = t e-3t sin²t

A: Simplify the given function first in such a form that the formulas of Laplace transform can be…