Take the Laplace transform of the following equations (you may use tables): d²x dt² a) dx +2+3x=1 given x(0)=1 x(0)=-1 dt

Q: Find Laplace transform of the function t2Sint.

A: We have to find the Laplace transform of the function t2sint that is Lt2sint Use Laplace transform…

Q: Q2. Find the Fourier transform of the function S2x e- 0<x <1 otherwise f(x) = %3D

A: The given problem is to find the Fourier transform of given function, we have to use Fourier…

Q: Find the Laplace transform of the following: 1. f(t) = e-2t+5) sin³(8t) 3

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Q: Q: The Fourier representation of a function f(x): f(x) = {-10 V, 10 V, ーTくX x > 0 40 sinx sin3x…

A: Given f(x) = -10v.  When -π &lt; x &lt; 0              = 10v when 0 &lt; x &lt; π.   Graph of this…

Q: t, 0st<3 t2 3 f(t) %3D 0, F(s) = %3D

A: F(s) = 1-e-3s(1+3s)s2

Q: Derive the Laplace transform for the following time functions: a. u(t) b. tu(t) C. sin wt u(t)

A: We have to find the laplace transform of the given time functions.   According to guidelines we…

Q: Use the step function to calculate the transforms of the functions below. Evaluate at s = 1.

A: The transform of the function f(t) is represented as F(s), and it is defined as ∫0∞e-stf(t)dt, where…

Q: 2. Determine the Laplace transform of the function rsinr using the 2nd derivative theorem.

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Q: Find the transforms of the given functions: Please see attachment

A: By the properties of Laplace transformations:

Q: i). ƒ (t) = ²) ² ii). ƒ (t) =t²sinh (21) (5–31

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Q: Solve the D. E. to the I. V. P. sinx(e-y + 1)x' – cosx = 1, y(0) = 0 %3D %3D (1 – e') (1 + cos.x) =…

A: We will find out the required solution.

Q: 2s2+10s F(s) (s + 1) s2-2s+5

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Q: e-9s F(s) = g2 – 3s – 10 ||

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Q: * + 3x + 6x = 0, x(0) = 0, x(0) = 3, x(t) =?

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Q: 1 Find the Fourier sine and cosine transform of ƒ(x)=

A: Use the Fourier Sine and Cosine transform table to obtain the result.

Q: Q4: Find the inverse Fourier transform of the spectrum: - 2s w S0 X (w) = 0 swS2 -- 0.W EIN I 0

A: Definition:

Q: Determine the Laplace transform of the function tcost using the 2nd derivative theorem.

A: Laplace Transform: Given a function ft defined for all real t≥0, the Laplace transform of ft is a…

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

A: To solve given question first we write the partial fraction decomposition of given function and then…

Q: How to solve the Laplace transform of the following equation: W(t)=cos(3t) - cos(7t) Please write…

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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: SOLVE STEP BY STEP IN DIGITAL FORMAT 2. Find the transform of the equation x² + xy + y² = 1 when the…

A: Let us consider the equation to transform the coordinate use  x=Xcosθ-Ysinθy=Xsinθ+Ycosθ

Q: F(s)= F(s)= (s +1)e$• (s +1e-Ss s°(s + 2) S

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Q: B: Find the Inverse Laplace transform of the following functions: (b) F(s) = = S-1 2s²8s + 11

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Q: Find the Laplace Transform of the following functions:

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Q: The approximated value for e using the Maclaurin series expansion coasidering a true relative error…

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Q: Find the Fourier transform of the function : S (t) = e-x2 %3D

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