When using Laplace transform to solve the IVP :Xn = 'n u(x,0)= - x. t>0 Then u]= 1 - SX e a. SX ce Sx s2 b. 1 s2 1 -SX+ - Sx S O d. 1 - SX - --e SX e. S 1 SX s- O f. e SX -- O g. - SX + e - SX -ce e O h.

Q: Compute the Laplace transform. Your answer should be a function of the variable s: s(πt)} = c{₁+ +…

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Q: Find the inverse transform of the given functions: 4s2 -4s+1 1. F(s) = (s3-4s2 +s+6)(s²+5) 3s-6 5s…

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Q: Exs- Find and sketch the signal Corresponding to the z-tranoform function لن T+37722=2

A: Break the given z transform into partial fractions and bring the terms into recognizable forms of…

Q: Find the inverse Laplace transform of the function as + b H(s) = (s – a)2 + 32 °

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Q: 4] Find the Laplace Transform of f(t) = { S-1 (-/= + 5 = /₁1) (1te - 1/₁1) (a) (c) S S - I (b) (d) S…

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Q: Obtain the inverse Laplace transforms of the following function 5(s+2) F(s) = (2+2s+1) 10 5texp…

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Q: L[2t2 + 5 – 3 cos nt), t > 0

A: We use the Linearity property and table of Laplace transform to find the answer of the given…

Q: Q3: Find the following Fourier Transform using properties only: F{e=2t+6+j2(t=3)u(t – 3)}

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Q: s2-2s -n: (s-+4)(s-+4s+5)

A: Given: s2-2ss2+4s2+4s+5

Q: ii) F(s) = (- + 10s + 2.

A: The inverse Laplace transformation is below :

Q: 4. Determine the Fourier transform of the given function: 1 (t) = {2t - t, 2t - 1, 0 < t < 1 0<t<2…

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Q: (c) Find the inverse Z-transform of Y(2) (32 – 1)(2+4)*

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Q: Find the inverse Laplace transform of 7s + 3 82 + 17 8 >0

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Q: Determine the Laplace transform of the equation f (x) = 2e-"sin4t 16 A s2+ 4s + 20 20 B s2+ 4s + 20…

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Q: = Find the inverse Laplace transform f(t) = £¹{F(s)} of the function F(s) = f(t) = = L 6s+2 s² + 100…

A: The function: Fs=6s+2s2+100. We have to find the inverse Laplace transform of the given function.

Q: Write down the qualitative form of the inverse Laplace transform of the followir functions. For each…

A: The given equation of  Laplace transformation is: Poles are the zeros of the denominator the…

Q: find the Inverse Laplace Transform 5² +95 + 6 s(s+ 1)(s + 3)

A: The Laplace transform of the function f(t) is represented as F(s) or L[f(t)], it is defined as…

Q: Show that the finite sine transform of , 0 < x < n is (- 1y*'- p

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Q: Find fourier cosine transform of for 0 1

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Q: B- Find Inverse Laplace transform of the following functions F(s)= 2s-7 (s+ 6)(s² + 4) G(s) = s(s² +…

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Q: Calculation: Rewrite the given function. Y [s] = 2s+3 s²+s+1 2s+1+2 e

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Q: Use Laplace transform technique to solve y+2y+2y=e, y(0) = 3, y (0)=-3

A: We need to use Laplace transform to solve this differential equation.

Q: 1 F(s) : (s-2)(s-4)(s-8)

A: Use the Laplace table.

Q: Q6/ Find the Inverse Laplace Transform 1 2- L-1 (s²+9).

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

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Q: Compute the inverse Laplace transform of the following functions. -2s 2s³+3s²+2s+27 (s²+9) (s²+1)

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Q: sx 14-X Find the Fourier transform of function f(x) = , 0<x< 14 14 < X <16

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Q: Solve for the inverse Laplace transform of st+3s"+s? 01+3t + 2t2 O 2+6t- O01+3t + t? O1+3t + 3.

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Q: i) F(s) = ii) F(s) = (s + 3)(s² + 16), s² + 10s + 2.

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Q: X(z) = z² N N (2--/-)² (2-²) 3/

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