Use the definition of the Laplace Transform and the properties of the Dirac Delta generalized function to compute the following expressions. (a) C[88(t − 2)] = Σ - (b) £[-98(+ + 1)] = (c) £ [5t* δ(t − 4)] - = Σ M

Q: 1. Find the Lapace Transform of the function f (x) = x. Show all your steps and be sure to use…

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Q: # "S" Domain "t" Domain 1 4/5 (S+ 1)² /s 2 3 2/S + 4/s5- 1/(S +2) 1/ (S + 81) 5 (S+ 2) / (S² + 3)

A: The solution is given as

Q: F(s) = (8-2)e-* 8²-48 +3

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Q: Q1. Find the Fourier of the function in Fig.Q1 f(x) -a a x -a Fig.Q1

A: Q1.The function in Fig.Q1 is a sawtooth wave. The function can be defined as:f(x)=πa​xFourier Series…

Q: Q9. Use Laplace transform to solve the ODE. X-4x +3x =-8cos4t, x(0) =0, x(0) = 0 %3D

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Q: a. Find Fourier transform for the following function l(x): -1 15 |(x) = {". (Hint: \r| =r for r> 0,…

A: The given function is  l(x)=1 if -1<x<10  if |x|>1 We know that the Fourier transform of a…

Q: 2. Determine the Laplace transform of the given function using the Table coshbt te3t sin2 t

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Q: If F(s) = 1 (S-1)√s' Find L{log t} Find L-¹{F(s)}.

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Q: (b) Find the inverse Fourier transform of the following: (11) 1 √w√2π (3+jw)

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