If L[x(t)] = X(s) and x(0) = 5, x'(0) = –4, find the Laplace transforms of the following expressions. dx a) dt 10x b) 5dx - 3 + 2x dt2 dt c) d²x + 10- + 10x dt dt2

Q: Determine the Laplace transform of f(t) = 5sin 2t - 6t * cos 2t

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Q: Solve the Laplace Transform of the equation f(t)= sin3t/t

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Q: Find the Laplace Transform of h (t) = t2 e-3t (*+3)" 4. (8+3) (8-3)" (s13)"

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Q: Find the general solution to the ODE d^2y/dt^2−dy/dt−20y=0.

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Q: Find the Laplace transform of the equation: y′′−4y=sin2t when y(0)=0, y′(0)=2 choices: a.)…

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Q: a) Find the Fourier transform of 4 f(t) = e tu(t) + -tu(t) + ²9.

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Q: Q2 \ Determine the Laplace transforms of the following function: t | e-4tt sin? 3t dt L

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Q: Find the inverse Laplace transforms: Y(s)=(2s+3)/((s+5)^2+4)

A: 2e−5t(4cos(2t)−7sin(2t))​Explanation:

Q: Find the Laplace transform of the function f(t)= (5e/t+4t)using the table of known as2+bs+c…

A: We first find Laplace transform and then comparing we find the value of c.

Q: Derive the Fourier spectrum of a signal that is given by z(t) = forect (2T) exp(−j10t + jt) dt.…

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Q: L{e2"sin2t + etcos3t}

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Q: So (sinh (-2t)e¯') u(t)

A: We shall find the Laplace transform of∫0tsinh-2te-tutdt that is L∫0tsinh-2te-tutdt First Shifting…

Q: Find Laplace transform of the function f(t) = cos(2t + 3)+e¬'u(t – 4) + tcosh²2t

A: Use the following formulas while calculating the Laplace transform of the given function.…

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: In a equation, f(x) = 3 sin 3x - 2e-2x Calculate the Laplace transform

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Q: The Fourier transform of the function f(t) = 2e-2t cosh 2t u(t)is: 2 4 A- πδ (ω) B- πδ(ω )+ j2w+w?’…

A: We have to use formula for Fourier Transform.

Q: 2. Calculate the inverse Laplace transform: 2s (a) C- C-¹ { 25+32 }; (b) C-¹ ( 25-3₂} 2s L-1

A: We have to find the Laplace inverse transformation of and

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: Let x(t)=5sinc(1.5t) +6cos(7/2) and h(t)=4sind(). Determine y(t)=x(t)*h(t) using Fourier Transform…

A: Let  and We need to determine y(t)=x(t)∗h(t).To solve this problem, we list the Fourier transforms…

Q: • Let: X₁ (jw) = 2nd(w) + nd(w − 4ñ) + ñ8(w + 4π) • Use the inverse Fourier Transform to find x₁(t)…

A: Introduction: Like other integral transformation, Fourier transformation has also its inverse. In…

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: f(d) = 2e+d[2 sin(4d) cos(2d) – 2 sin(2d) cos(4d)]

A: The given problem is to find the Laplace transform of the given function, we can use basic…

Q: Compute the Fourier transform of the following function: f (x, y) = e-(1x-y|+|x+y[)<+

A: Calculate Fourier transform: Fu,v=∫y=-∞∞∫x=-∞∞fx,ye-2πjux+vydxdy…

Q: f(t) = tg'(t)

A: The solution is given as

Q: Find Fourier transform for : A) f(t) = e-3t cos² (3t) B) f(t) = te tu(t - 3)

A: (A)Given f(t)=e−3tcos2⁡(3t).Now, we'll find the Fourier transforms for individual terms.The Fourier…

Q: -2sin4t Determine the Laplace transform of the equation f (x) = 2 e´ 10 A s²+4s+20 8 B s²+4s+ 20 20…

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Q: Show that x(t) * u(t) x(t)dt %3D and find its Fourier transform.

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Q: Q1. a) Derive the Laplace transform of 3e4t from first principles (i.e. without using the list of…

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Q: 2+5( jw) (jw)' +3( jw)–10 a- F(w)=-

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Q: 3. Find the inverse Laplace transform. a) 8s2 − 4s + 12/s(s2 + 4)

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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: Q1) a) Find L[ (k - ht)².t²] RI Find the Laplace transform of: f (t)= et, cos² (3t)

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Q: I the Fourier transform of f(t)= 3sin5t +4cosl %3D

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

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

Q: Find the Fourier Transform of Sel2t -1<t<1 f(t) = {e1²t 0 elsewhere

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Q: (4) 3 2s-4 1 s2+4s+4 s+2 s2+4s+5 5s-6 s2 –3s

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