Prove the following continuous time Fourier transform relationship. sin(at) 1 X(N) = Continuous Time x(1) = = sinc(t) nt otherwise Fourie Transf.

Q: 1. Find the laplace transform of sin(t)sin(2t) sin(3t), using est f(t)dt. F 1-4 3 1 r are. ².2.

A: As per our company guideline we are supposed to answer only one qs kindly post remaining qs in next…

Q: Find the Laplace Transform of f () =2 sin a +3 cos 2z.

A: This is question of laplace transform . Solution is given below

Q: e-2t cos 3t cOS

A: The given question is related to Laplace Transform. The solution is explained below.

Q: Examine the discrete time Fourier transform of sin) 5nn, .cos( 2 x[n]

A:

Q: Find Laplace Transform of the following function by definition only (Show all steps on integrals)…

A:

Q: Find the Laplace Transform: 2x2 e* cosh x

A:

Q: a) Solve the initial value problem using Laplace transform IMUTM UTM UTM IM UTM TM UTML

A: First we take Laplace transform of given differential equation and solve.Then solve for inverse…

Q: Find the sine transform of a function of x which is equal to sin x for 0 <x<a and 0 for x2a.

A:

Q: 8 The inverse Laplace transform of the function is sin(3t) (A) t – 3 sinh(3t) (B) t- 3 sin(3t) (C)…

A:

Q: Find the Fourier transform 1-x, | x | 1 sin x Cos X CoS x Hence evaluate dx.

A:

Q: Find the Laplace transform of: 1. f(t) = e(-3t) sin(2t) cos(3t) cosh(t)

A: Given that 1) f(t) = e-3tsin (2t) cos (3t) cosh (t) 2) f(t) = 1+sin t + (8t)15 + t2cos 3t We have to…

Q: * Find the inverse Laplace transform for-1 1 F(s) s – 2s + 5 1 -e²"sin2t 2 1,2'sin2t e'sin2t خيار 1…

A:

Q: 2(+-3) cos (t-3) y ct) : Sin 2t cos 34

A:

Q: Find the Fourier sine expansion of f(x)=x² (3L– 2x) on [0, L].

A: The function f(x) is a rule that associates or fixes a number to the particular point x. If y=f(x),…

Q: 7. Obtain the Fourier sine transform of the following functions: sin wx (c) x² +1' w > 0

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

Q: 1. Find the Fourier transform of this rectangular pulse X (w) and show that sin πωτ X(w) = A² 2.…

A:

Q: . Find Fourier cosine transform of - and deduce that 2. bx e 1 e V2m log р ға cos px dx

A:

Q: 7. Given that the Laplace transform of te is F(s) =- (s + k) Laplace transform of te" without using…

A: The solution is given as

Q: 8. Find the function whose Fourier sine transform is the following function. S[u] - 2 0 x = [1, 2],…

A:

Q: 4. Solve for Laplace transform of f(t) = t^5 using long method

A: This question is based on Laplace transform formula.

Q: WHAT IS THE FOURIER EXPANSION OF THE PERIODIC FUNCTION WHOSE DEFINITION IN ONE PERIOD IS: F(t) = for…

A:

Q: Determine the Laplace Transform of cos*t

A: cos3t≡(cost)(cos2 t) cos3t=cos(1−sin2 t) cos3t=cost⋅1/2(1+cos2t)…

Q: e-t(cos 4t – 2 sin 4t)

A:

Q: 468 CHAPTER 14 The Fourier Integral end TransforAS sin(x) for -4sx 4 5. S(x)= * for-100 srs100 0 for…

A: In the given question we have to find the fourier integral of the given function f(x) = x2     for…

Q: Solve the laplace transform 3x-6x= Sin 2t %3D given when t=0

A: Use the laplace transformation table and derivative formula

Q: Use Laplace transform to solve the given IVP. 3. у" — у' %—D еХ cos x, у(0) %3D 0, у'(0) — 0

A: We have y''-y'=excosx  , y0=0 , y'0=0 Now,  Ly'=sYs-y0Ly''=s2Ys-sy0-y'0 Take Laplace transform on…

Q: Find Laplace transform of te-t cos t

A: Using Laplace formulas we will find the Laplace transform of  t e-t cos t

Q: 1. Show that the function 2t et cos (et“) is not of exponential order, however its Laplace transform

A:

Q: 2. Determine the Laplace transform of the given function using the Table coshbt te3t sin2 t

A:

Q: Find the Fourier transform for S(2)%3D sin a, 2 0.

A:

Q: * Find the inverse Laplace transform for-5 1 F(S) S + 25 5 sin(5t) 1 sin(5t) 1 s O 0 خیار 3 sin(5t)…

A:

Q: (3) A signal has Fourier transform as, 1 sinc (2w X(w) sinc + 2. Compute x(t)

A:

Q: i) Find the Fourier sine transform of (sinx, 0a %3D au Courier Transforms, Calculate

A:

Q: What is the Laplace transform of x (t) = e^- t cosπt ? Select one:

A:

Q: Q6) (a) Prove that Fourier cosine transform of f(x) = cos(x), 1 sin 3(p-1), sin 3(p+1) p-1 p+1 +…

A:

Q: Σ 4 NITX (пл)з (1- сos(пп)) sin. L f(x) = n=1 8

A:

Q: Use the Laplace transform to solve the following IVP y - y = 2 cos 5t, y(0) = 0 %3D

A:

Q: Find Fourier cosine transform of: and deduce that - ax -e p²+ b? 1 log P+ /2T cos px dx = 2 p +a

A:

Q: Show that (a) L-1 = sin(at) - tcos(at) %3D (s²+a²)²) (where L indicates imverse Laplace transform)…

A: L-11s2+a22=12a2sin(at)-12a2tcos(at)

Q: 5 The inverse Laplace transform of the function sin(2t) (A) 1 – 2 sinh(2t) (B) t- 2 sin(2t) (C) t- 2…

A:

Q: 1.) Give the Fourier transform of the function f. Sx ha x = [0, 1] f(x) = 0 otherwise.

A:

Q: (7) Find the Fourier transform of the following functions: { {: cos x, if 0 1 (ii) f(x) = 0,

A:

Q: ve an expression for the x(t) and Determine the Fourier transform of the signal x(t) shown in Figure…

A:

Q: Prove the following continuous time Fourier transform relationship. Continuous Time 2л x(t) = E…

A: Given, xt=∑n=-∞∞δt-nT. Now, xt=∑n=-∞∞δt-nT is a periodic signal with period T. So, converting in…

Q: 3. Find the Fourier transform of f(x) = {1, |x| 1 Also evaluate .00 Sinx dx

A:

Q: 1. Solve the Laplace transform of the following: iii) t'sinh(3t)

A: Given that: t4sinh(3t)

Q: 4. Use the dilation principle to find the Laplace transform of 1- cos 5t cos t given L{- In g² +1 t

A: We want to find Laplace transform of 1 - cos5tt Given L1 - costt = 12lns2s2+1

Q: (b) Using Laplace transform, evaluate te -2t Cos 2t dt 0.

A:

Q: 5. * + 9x = cos 2t

A: