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: 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)= (14t)-3e-7t cos(8t) - (2t-6)²

A: Here given function ft=14t92-3e-7tcos8t-2t-62orft=14t92-3e-7tcos8t-4t2-36+24t Use the basic property…

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: d. cos wt u(t)

A: The given problem is to find the Laplace transform of the given time function. Given f(t)= cos(wt)…

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: 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

A:

Q: Express the following functions mathematically and find their Laplace transforms. f(t) Slope = 1 -1…

A: (a)The graph represents the function: f(t)=0        t≤0t-1   t≥0 The function is discontinuous at…

Q: f(t) = 6te-3t + te-5t sin5t + t² %|

A:

Q: Write the function in terms of unit step functions. Find the Laplace transform of the given…

A: Inverse Laplace transformation of the pice wise function

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

A:

Q: Kind the haplace transform of f(t)=78(t-½)Cost.

A:

Q: Find the Fourier Sine Transform of the function f(x) = (ae-4* + be-3* + ce-2*) if x> 0 if a = 6, b =…

A: The given problem is to find the Fourier sine transform for the given function with given unknown…

Q: e-9s F(s) = g2 – 3s – 10 ||

A:

Q: Vanessa invested $11,500 into a fund earning 7.50% compounded monthly. He plans to withdraw $650…

A: 1) Total fund will be available after 5 years Just before first annuity withdrawal :   Amonut = P *…

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…

A:

Q: Find the Laplace transform of the given function; b is a real constant. f(t) = cos(bt) Your answer…

A: Given: The given function is ft=cosbt, where b is a real constant. To find: We have to find the…

Q: Laplace transform of the following functions: 2. t5/2 sinh 4t

A: We find the Laplace transform of the given function in Problem 2

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

A:

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:

A: