Question 1 (a) For the function 0st<3 f(t) = - 2) t23 use the definition of the Laplace transform to find L{f(t)}. (b) ( ) Find the inverse Laplace transform 2 2s+3 C -5)(s+3) 82 +

Q: (2) Apply inverse Laplace transform and find f(t) of the following: 6(5+3) S (5+1) (5+2) a) F(s) =…

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: Find inverse Z-transform 1+- X(z) = (1 - -)*

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Q: 5s + 20 F(s) = s2 + 8s + 97

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Q: Q8 Find the Fourier transform of the following functions: p,-1<x <1 f (x) = 0, otherwise p-x,-1<x <1…

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Q: The Fourier transform of a function } (t) iš defihed by F(w) = f(t)e-jwtdt %3D a) Using the above…

A: The Fourier transform of a function f(t) is defined by F(ω)=∫-∞∞f(t) e-jωt dt 1) We have to find the…

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: 2. (a) For n 2 0 write out the fint four terms of the sequence z(n) 3(-3)" and then use the…

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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: 2s – 7 - F(s) = %3D (s – 4)(s + 6)

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Q: Find the Fourier Sine Transform of the function f(x) = (ae-4* + be-3* + ce-2*) if x> 0 if a = 6, b =…

A: The given problem is to find the Fourier sine transform for the given function with given unknown…

Q: Find the inverse Laplace transform C-{F(s)} of the function 8 F(s) (s – 5)³ NOTE: The answer shouid…

A: Given that, F(s)=8(s-5)3 The Inverse Laplace Transform of the function is determined as shown below.…

Q: Find the function f(x) that has Fourier transform (k) = (1+k4)-1.

A: Here we have to find out  .Now from definition of inverse fourier transform , to evaluate this…

Q: Find the inverse Laplace transform L-{F(s)} of the function F(s) s2 + 9s – 10 NOTE: The answer…

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

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: Please show all solution with explanation. thanks

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Q: 2-find the laplac transform for the function: t² (u-1)

A: Introduction: Laplace transform is named in honour of the great French mathematician, Pierre Simon…

Q: Q2/ from definition of Fourier transform, show that rect (t-5) is sinc (w/2)e-/2w

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Q: 2s2 – 3s + 5 - Find the inverse Laplace transform for s2 (s2 + 1)

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Q: az"¹)]sin(a @)-¹ + a² az-1)2]sin(a w)₂-¹ + a² az-1)³]sin(a @)²-¹ + a² -(az-1)³]sin

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Q: XP+2ap +2a') ple 23: Find the inverse Fourier sine transform f(x) of F, (P- ap

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Q: Calculation: Rewrite the given function. Y [s] = 2s+3 s²+s+1 2s+1+2 e

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Q: pply the theorem L(f* g) = L(f)L(g) to find the inverse Laplace transform; also do it in mother way…

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Q: Find the inverse Laplace transform f(t)= C1 (F(s)) of the function F(s): 36)}-Oh f(t)=c-1 {-(; 6 +64…

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Q: Example F(s) = find the inverse Fourier transform: 6(s + 10) (s + 5)(s+8)

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Q: If the Fourier transform of f(x) is f(k): f(x) x (a) Find the Fourier transform of in terms of f(k).…

A: Given that the Fourier transform of  is .We need to find the Fourier transform of  in terms of .We…

Q: Q6) (a) Prove that Fourier cosine transform of f(x) = cos(x), 1 sin 3(p-1), sin 3(p+1) p-1 p+1 +…

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Q: Inverse Laplace transform of s2+9 is given by O cosh(3t) O cos(9t) O cos(3t) O sin(3t)

A: Find the inverse Laplace transform of ss2+9 we know that L-1ss2+a2=cosat