Find the Inverse Laplace Transform of the following functions t- a Ans. f(t)=- t> a A) F(s) = t< a (cos(2t) t> T se В) F(s) 3D Ans. f(t)= s? +4 elsewhere s+12 C) F(s) = Ans. f(t) = 3- 2e 1- 3sin(t)) s? + 4s

Q: Recall that Q denotes the set of rational numbers. Show that there does not exist a strictly…

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Q: Q.5A/Find Laplace Transform of the following functions 1.f(t) = 6e-6t + +5t3-9 2./(t) = (42marke)…

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Q: 2C

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Q: cos x, 0 a

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Q: (2 + + +9 4²5 ) (7 + 27 ) = (+) 5 7 Find Laplace transform of the function.

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Q: a) Consider the following function UTM UT Cos t, cos 2t, 0 T. UTM ii. Hence, find its Laplace…

A: The given problem is to express the given function in terms of unit step function and also find the…

Q: cos x, 0a

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Q: d. Find the Laplace transform of f(t) = sin22t + cos22t + 1 ۵. 4/s b. 3/s 2/s 1/s ن d. 3t-5t²-2(t-

A: Given that the function ft=sin22t+cos22t+1

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: 2. Determine the Laplace transform of the given function a) f(t) = e³¹t4 b) f(t

A: Laplace transform

Q: Let F(s) be the Laplace transform of f(t) = cos (k(t – 7)] e" sin(37)dr, where k is a positive…

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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: 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: 9-12s-4s2 C. (s2+4)2 +12s-2s2 (s2+4)2 9+12s-4s? D. (s2+4)3 -12s-2s? (s2+4)3

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Q: Apply the properties of Laplace transform including the linearity property, shifting property, and…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Find the Inverse Laplace Transform of the following functions 3s? – 2s–1 (s- 3)(s² +1) A) F(s) =…

A: As Multiple Questions are given , I will solve the first one Only :   We are given…

Q: Find the Laplace Transform of the following functions: 1. f(t) = (2e-4t + sin t)²

A: We have to find the Laplace Transform of the following function. 1)  f(t) = (2e-4t+sint)2

Q: Find the laplace transform of t sin (t) A. 2s/(s2+1)2 B. 1/s2(s2+1) C. 1/s2 + 1/s2+1 D. -…

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Q: Apply the translation theorem to find the inverse Laplace transform of the following function. 6s +9…

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Q: 21 = 0 with . and = 4 with v2 = Write the solution to the linear system r' = Ar in the following…

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Q: 2. Determine the Laplace transform of the given function. a) f(t) = e³¹t4 c) f(t) = est sin(3t) e)…

A: Recall the formula of Laplace transform: For any non-negative integers L{tn}=n!sn+1 .The property of…

Q: Find the Laplace Transform A- f)=tcos(@r) B- f(1)=tsin(@t) C- f(t)=tcosh(at)

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Q: cos 4t-cos 2t 3. f(t) = t

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Q: 1. Find the forier tansform of f(t) = 8(t) + 2e-3lt| %3D

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: exp (exp (– in),

A: The objective is to find the value of expexp-iπ

Q: The question involves finding the inverse Fourier Transform of the following functions:

A: see the attachment given below for details.Explanation:

Q: 2. Find the Laplace transform of the following functions. (Use the table.) (a) g(t) = 2e“ + 21²e“

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Q: y -7y +10y= 9cost+7sint, 5, y =-4 2

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Q: 1 Y(s) : s2 + 7s + 10 a. y(t) =(e-5t – e24) b. y(t) =(e-5t + e²') c. y(t) =(e5t - e-2t) d. y(t)…

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Q: Show the following Fourier Transform and F{tri(t)}(f) = sinc²(f) F{e-t²}(f) = e-f² You may use the…

A: Given: Here is the given Fourier Transforms,  Ftritf=sinc2f and  Fe-πt2f=e-πf2