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: Find the inverse Laplace Transform of: 11 5s 3 1 F(s) s2 + 3 s2 + 9' 5s – 7 s4

A: Use the formulas below to calculate the inverse Laplace transform.

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

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Q: B: Find Laplace Transform of f(t)= cos3t By DEF.

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Q: Find the Laplace transforms of the following function: g(t) = 7e-#(6t – e*)².

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Q: b) Find the inverse Laplace transform of the following function: 3s +6 F(s) = s² +9s + 5.

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Q: Find the complex transform of F(x) = e¬l\l, –∞ < x < ∞

A: Complex Fourier Transform or Fourier Transform: Let Fx be a function defined on R Then Complex…

Q: 6. Find the inverse Laplace transform of the function (3²-²)(as + b) I(s) = (s² + a²) (s² + 3²)

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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: 2. Determine the inverse Laplace transform of F(s) F(s) = (25-18)/(s²+9))

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

Q: 1) x(t) = 1(t- 47T)

A: Solution 1: Given function is x(t)=1(t-4T)           (1) Let the z-transform of x(t) is X(z)…

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: Given 30<t ₹2 10 elsewhere find Fw), the Fourier transform of ƒ(t). Compute the values of F(0), F(1)…

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Q: Calculate r1(t)·r2(t)] and dt [r1(t) × r2(t)] first by differentiating dt the product directly and…

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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: 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: find the Laplace transform of t²cos(wt)

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Q: 2) find the fourier transform x(t) = u(t) x(t) ulzt) x²(t) = u(+ + 5) -

A: xt=utxt=u2txt=ut+5xt=ute-jw0t

Q: 5. Find the inverse Laplace transform of the function as + b H(s) : (8 – a)2 + B2"

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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: If F(w) is the Fourier transform of f(t), then the Fourier transform of g(t)=3e²jt f(t) may be…

A: If Fω is the Fourier transform of f(t), then using the linearity property, it can be written that…

Q: 5. Find the inverse Laplace transform of the function H(s) = as + b (s-a)² +32° a = 9,b= 10, a = 4,8…

A: We have to find the inverse Laplace transform of the function H(t)=as+b(s-α)2+β2 when a=9, b=10,…

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: 3. Find the inverse Laplace transform of the function (a - B)2 2(a - B)3 (s - a)(s – B)3 a - B F(s)…

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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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Q: Find the Fourier transform of (а) f (г) %—D еxp (-ах?), () f (») — еxp (-а \x),

A: To find the Fourier transform of the below functions. fx=e−ax2 fx=e−ax

Q: Q6. Solve the following difference equation using z-transforms: Yn+1 + 3yn = 4√n-2, yo = 2

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