G(s) using the Convolution theorem is s? +1 The inverse Laplace transform of F(s)=- a) f(t)= [sin(r)g(1)dr b) f(t) = [ sin (t-r)g(r)dr c) f (t)= |sin (7)dr d) s(e)- [e(?)dr

Q: sform of s+2 s° (s+1)(=

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Q: (2) Apply inverse Laplace transform and find f(t) of the following: 6(5+3) S (5+1) (5+2) a) F(s) =…

A: Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: then prove that i) F, [ƒ (x) cos ax] = [f, (p + a) +f, (p a)] 1 ii) F.[f(x) sin ax] 2 [f. (p + a) –…

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Q: (a) Use the definition of the Laplace transform to compute L{cosh(at)}, where a e R\{0}. What's the…

A: Laplace Transformation: Definition: Let f(t), t≥0 be a function, then F(s)=∫0∞e-stf(t)dt provided…

Q: x2 , Ix1 a = find Fourier transform of f(x)=

A: To determine: The Fourier transformation of  f(x) = x2 ,     x<a 0 ,       x>a

Q: sin(t) Find the inverse Laplace transform of Let F(s) be the Laplace transform of f()= Y(s)= F(s-5).…

A: Inverse Laplace Transform: Let Fs be the Laplace transform of a function ft that is Lft=Fs, then ft…

Q: (A-1) L[2¬3 cos t] by s-shifting theorem (A-2) L[t e¬t cosh 2t] by differentiation of Laplace…

A: Given: (A-1) Le-3tcost (A-2) Lte-tcosht (A-3) Lsin2t·ut-π4 (A-4) L4t*e-2t

Q: I need help with this problem described below and an explanation for the solution. (Differential…

A: Step 1:Step 2: Step 3: Step 4:

Q: 5 sin 3 (t ), t > 4 6. If f(t) = 0, t <

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Q: 2 F(s) 4 e-2s + s2 3 e-s s2 a) Find the inverse transform of F (s) b) Sketch the graph of f(t) c)…

A: (a) Given that Fs=2s-3 e-ss2+4 e-2ss2 Applying inverse Laplace transform on both sides L-1Fs=L-12s-3…

Q: Solving the Logarithmic Equation: In(x + 2) + In3 = 2

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Q: FindiL [+ sin 5+] IDS a1) s (s*+25) C. S?-25 di) (5?+ 25)2

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Q: Find the Laplace transform of these functions: (a) e¯† cos t (b) e-" sin(rt) (c) e¯† sin(wt + y) (d)…

A: If ft is defined for all positive values of t and if ∫0∞e-st f(t) dt=F(s) , then Lf(t)=∫0∞e-st f(t)…

Q: Question 2 Find the linear approximation of the function at the given point. f(x, v) = 3 sinx - 7…

A: F(x,y)=3 sin x - 7 cos y at ( 0 , π/2)

Q: unctions f and g have Fourier transforms F[f] – and F[9] = That is the Fourier transform of, h(t) =…

A: Given: Ff=1w2+1Fg=e-w2 A Fourier transform is a mathematical transform that decomposes functions…

Q: The Laplace transform of f (t) = e2t sin(7t) + te¯3t is %3D

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Q: O [-5, -1) U (1,6] O (-5,6] O [-5, 6] O (-5, -1] U [1, 6] Find the domain of r(t) = (ln(t + 5),…

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Q: The Fourier Cosine transform of the function f(X) = {1, |x| a} a A 1/(/2n)*(cos(as)/s) B…

A: Given functionfx=1,x&lt;a0,x&lt;aFourier cosine transform of f(x) is given byFcfx2=2π ∫0∞ f(x)…

Q: Find the inverse Laplace transform s+7 F(s) S2 – 3s – 10 A) f(t) = ?e" +;e-7* B) {() = e* +e-** C)…

A: using:-  L-1 (1/(s-a)) = eat

Q: { x2, Ix1 a ||

A: Given function is f(x)=x2     x&lt;a0      x&gt;a let the Fourier transform of f(x) is F(s) So we…

Q: If v(r, y) is a harmonic conjugate of a harmonic function u(x, y) show that the function g(r, y) =…

A: Harmonic function: A two variable function ux, y is said to be harmonic, if the function is twice…

Q: Determine the Z-transforms of the following expressions (ii) (cos+isin)"

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Q: Question 2.i.) Find the Fourier transform of the function f(t) = 4e-7|| %3D 2.ii. What are the…

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Q: Question: - Find the Laplace Transform of the four functions? 1- f(t) = cos(t) [cos²(t)-sin²(t)]…

A: Since you have posted a multiple question ,I will solve the first question  for you. To get…

Q: 6s – 5 Find the Inverse Laplace Transform of F (s) s2+7 5 f (t) = 6cos(/7t). -sin(/77) _cos(/7 ) 5 B…

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Q: Find the Laplace transform of f (x) = 3 sin 3x – 2e-2x

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Q: - 3s2 + 21s 42 Find the inverse Laplace transform of F(s) : (s – 3)3 -

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Q: F(e) = 5 3 s-2 Find the inverse Laplace transform of F(s).

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Q: 1 t3e0.035t 2

A: Use the following formulae, to obtain the solution. Laft=aLftLtkft=-1kdkdskLftLeat=1s-addxxn=nxn-1…

Q: Find the Laplace transform of f (x) = 4 sin x + 6 cos 2x

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Q: Question: - Find the Laplace Transform of the four functions? 4- f(t) = St sin(t) e-Stdt

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Q: Laplace transform

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Q: Using the Laplace Transform find the function F{S), knowing that f(t)= 6et +sin(3t ) – 8cos(9t )

A: In mathematics, the Laplace transform, is an integral transform that converts a function of a real…