Problem 1. Using the table of Laplace transforms or any other method, compute the Laplace transforms L(f) of the following functions: (i) (ii) -8t f(t) = e² 8(t − 3)+4(t − 5)(t + 6) + 7 cos 8t+9e¯ +7e6t sin 5t + 4t³ e-2t, if 1

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: Find the Laplace transforms of the following functions: 3 -4 (s + 3)² + 16 4s2 – 4s + 2 (s – 1)3 13…

A: Since you have posted multiparts questions and we can answer 3 subparts. So answered 1, 2 and 3.

Q: 3. (a) Find the Laplace transform of (i) f(t)=17te-2-3 sin(9t) (ii) fo

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: . Using a hand calculation, find the Laplace transform of: f(1) = 0.0075 – 0.00034e -2.5t cos(22t) +…

A: Since you asked multiple questions so as per guidelines we will solve the first question for you. To…

Q: 1) f(t) = e3t+ sin²t +6 cosh /7t -3t²

A: We'll answer the first question since the exact one wasn't specified.  Please submit a new question…

Q: From a Laplace Transform form, we have the following expressions: s - w I) L{ewt cos(ßt)} (s – w)2 +…

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Q: Solve the following Laplace transform 1) f(t) = sin (21) cos (21) 2) f(t) = cos¹ (21) 3) f(1) = te…

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Q: 1. Find the Laplace transforms of the following functions using the table of Laplace transforms and…

A: Solution :-    The given functions are                 (a)   f(t) =  4t2 - 5sin(3t)…

Q: Compute the Laplace transforms of the following functions; i. f(t) = 6e-5t +e3t + 5tª – 10 ii. g(t)…

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Q: Signals x (t), h(t), and g(t) are given as follows: x(t) = −2. sin(3t) πt h(t): sin(3t) πt g(t) = −…

A: Using the characteristics of the Fourier Transform and the provided signals x(t), h(t), and g(t), we…

Q: A new flag pole for a school campus measured 25 2/3 feet. It was put 4 1/2 feet into the ground and…

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Q: Use appropriate algebra and Theorem 7.2.1 to find the given inverse Laplace transform e-s s(s+1) a.…

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Q: Consider the table of Laplace transforms provided in the lectures and the result above. Using that,…

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Q: 1. f(t) = e-3t-2| %3D

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Q: B) Find Laplace transform of each of the following: 1) f(x) = 0.5e3x + cos(bx) ex sin(cx) - at 25 2)…

A: Solution of the given question is like as

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

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Q: Find the inverse Laplace transform L¯¹{F(s)} of the function F(s) L-¹{F(s)} = = 6 (s − 1)³ NOTE: The…

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Q: Apply Fourier transform, jw F(w) = F₁ (w) + F₂ (w)...... equation 2 |F₁(t) = −8(t + 2) +…

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Q: Use the formula £{t" f(t)} (s) = ( – 1)" – (L{f}(s)) to help determine the following the…

A: We will use formula for derivative of u/v and given formula to solve as follows

Q: Apply Fourier transform, jw F(w) = F₁ (w) + F₂ (w)...... equation 2 F₁ (t) = −6(t + 2) +…

A: What is Dirac Delta Function: The unit impulse, sometimes referred to as the Dirac delta…

Q: : Find the Laplace transforms of (i) (t – 2)°u(t–2) (ii) e¯"u(t - 2)

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Q: (a) F(s) = 2s (s¹ +24s² +144)

A: Since you have asked multiple questions here, we will solve the first question for you. To get the…

Q: Q3: Find the solution of the Laplace transforms of the following functions: -3s2-12s-8] L-1 1)…

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Q: Find the Inverse Laplace Transform. F (s) = 6s-54 82 +16

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Q: 2. Find the Laplace and Inverse Laplace transforms of the followings: (a) cosh(t)sin(2rt): Hint(cosh…

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Q: Find the Laplace transforms of f(t) = e(3t-7) cos3(6t).

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Q: Find the Laplace transforms

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Q: 9.) The Inverse Laplace tra (A) In(s² - 2-3 (C) //e+ + 3/e³1

A: Inverse Laplace transform of the function