DEFINITION 7.1.1 Laplace Transform Let f be a function defined for t 2 0. Then the integral L{{t)} = e-s*f(t) dt is said to be the Laplace transform of f, provided that the integral conve to find L{f(t)}. (Write your answer as a function of s.) So, ost< n/2 t2 π/2 f(t) = | cos(t), L{f(t)} = (s > 0)

Q: Find the Laplace transform of the following: 1. f(t) = e-2t+5) sin³(8t) 3

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Q: t, f(t) = 2t - 1, 0, 0 < t < 1 1 < t < 2 otherwise

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Q: F(z)=z tan:

A: note : As per our company guidelines we are supposed to answer ?️only the first question. Kindly…

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: Find the Laplace transform of f (t) = t 2 7-t 0 if 0 7

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Q: Find the inverse Laplace transform using the inverse form of the convolution 1 theorem L¯+ {(8?+1)

A: The convolution Theorem gives a relationship between the inverse laplace transform of the product of…

Q: 2.x²y"+xy'–3y= 0,x>0

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Q: Show that the Fourier transform of f(t) defined by: -3, -a < t < 0 3, f (t) = 0 <t<a Elsewhere where…

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Q: 3- What is the Laplace transform of each of the functions shown in Fig. 1. f(1) 4 f(1) A с K b 0 a…

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Q: Find f(x) = f a-1x1 0 the Fourier a-1x1, Hence prove transform Ixl <a , Ixla that 1 (sin t t 0 2 of…

A: Given f(x)=a-x,x&lt;a i.e., -a&lt;x&lt;a                   =0,         x&gt;a i.e., x&gt;a, x&lt;-a…

Q: A Fourier transform is another integral transform often used in higher mathematics. The Fourier…

A: Given Fourier transform of the function ft with respect to t Fft=∫-∞∞ft e-iωt dt Fω=∫-∞∞ft e-iωt dt…

Q: f(t): = tan(-7t) cos(-7t) + sin (−8t) e -3t cosh (-4t), 1 + 5 7 +=t5 + sinh (6t)

A: The given problem is to find the Laplace transform of the given function f(t).

Q: (k) f(x) =X[a.b](x) eiaz,

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Q: Use appropriate algebra and Theorem 7.2.1 to find the given inverse Laplace transform. (Write your…

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Q: Given 30<t ₹2 10 elsewhere find Fw), the Fourier transform of ƒ(t). Compute the values of F(0), F(1)…

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Q: Prove that Fourier cosine transform of f(x) = cos(x), 0<x<3 is: 1/27 (³ sin 3(p-1), sin 3(p+1) p-1 +…

A: Introduction: A Fourier remodel (FT) is a mathematical remodel that decomposes features relying on…

Q: If F(s) = {f(t)} and n = 1, 2, 3, . . . , then L{t^f(t)} = (−1)n d^_F(s). dsn Evaluate the given…

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Q: Use appropriate algebra and Theorem 7.2.1 to find the given inverse Laplace transform. (Write your…

A: The given problem is to find the inverse Laplace transform of the given function and find the value…

Q: use the laplace transform to solve the following IVP x' (+) + x (+) = f (+) x(0)=0 1 where O te[1,2)…

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Q: Suppose the function f: R→ R has Fourier transform 1 f(p) = e-p². 1+ 4π²p² i. What is the Fourier…

A: As per the question we are given the Fourier transform of a function f(x) as f̂(p) From that we have…

Q: H(s) = 1 s³ +bs² (use integral rule)

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Q: Using the Fourier Transform table, find the Fourier transform of this signal: (d) x(t) = = 1 if 1 ≤…

A: Given function is Since we know X(ω)=∫-∞∞x(t)e-jωtdt

Q: Part I. Find the Laplace Transform of the following: t-e-3t 1. f(t)

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Q: Q5) Find the Fourier transform of: SCos(nt/t) for lel < x(t)=D .elsewhere) Sketch X(f) versus f.On…

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Q: Use Definition 7.1.1, to find (f(t)). (Write your answer as a fun £{f(t)} = (s > 0) on of

A: This is a problem of Laplace transformation.

Q: Using Table of Laplace Transforms, find the Laplace Transform of the following function: cot(-7t)…

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Q: Use appropriate algebra and Theorem 7.2.1 to find the given inverse Laplace transform. (Write your…

A: Here,  we have to find inverse Laplace transform of given function.

Q: Use appropriate algebra and Theorem 7.2.1 to find the given inverse Laplace transform. (Write your…

A: use appropriate algebra to find the given inverse laplace transform L-16s-12s2+ss2+1

Q: Use Theorem 7.4.1. THEOREM 7.4.1 Derivatives of Transforms L{f(t)} and n = 1, 2, 3, . . . , then If…

A: Please find the answer in next step

Q: 2s2+1 Find the inverse transform: F(s) s(s+1)2 A. 3 – e-t – te-t C. 1- e-t + 3te-t B. 3 + e-t +…

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Q: Determine the Fourier transform of the function f(t) = H (t)e-5t

A: Heaviside unit step function, H(t)=0,t&lt;01,t&gt;0By the definition of Fourier transformation,…

Q: Find the Laplace Transform of the following functions: 3. f(t) = = cos 4t-cos 2t t

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Q: Draw the graph and find the Fourier transform of f(t)=e-at, a>0.

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