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Q: The first two terms of a Fourier series of a general periodic function are F (t) 2 ; + [3 cos t + 4…

A: Given that, The first two terms of a Fourier series of a general periodic function are…

Q: Q1. Find the Fourier integral of the given function and discuss it at the discontinuity points 1-x'.…

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Q: 36 3€ Find the laploce transform of f'(E) = e^†cos (6t) - e cos (Gt)

A: To find the laplace transform of ft=e3t+cos6t-e3t cos6t.

Q: Q1) Find Fourier transform for the following functions: a) x(t) = 3 + (sin2wt)?

A: It is given that

Q: (A) Find Laplace transform of the function: f(t)-t sin ( 21+5) cos(24-7) = 2t 2t (B) What function…

A: Given: A) ft=t sin 2t + π2 cos 2t-π2  Find Laplace transform of the given function. B)…

Q: X Q6) Find the Fourier cosine transform of f (x ) = sin x , 0<x <A 0, otherwise

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Q: 1 – x? a) Find the Fourier integral of f (x) =- %3D |x| > 1 b) Use part (a) to calculate the…

A: We have the given function is f(x)=1-x2       |x|≤10              |x|&gt;1 From the definition of…

Q: 1- cos at Q6. Find the Laplace transform of following functions (a) t sin at (b) t

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Q: O Find Fourier Cosine transform of: CoS X oa

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Q: (b) Find the Fourier transform of the function given below 1– x? if |x|1 and hence find the value of…

A: Calculate Fourier transform: Fω=∫-∞∞fxe-iωxdx         =∫-111-x2cosωx-isinωxdx…

Q: 2s + 3 Find the Inverse Laplace Transform of F (8) s2+ 4s + 13 A f(1) = e2 2sin3t – -cos3t B f(1) =…

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Q: 3) Find the Fourier transform of the following signals L. x(t) x(t) + 3 + 2 -2 2 -1 -1 1 -2 using…

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Q: (26) Denote the second Fourier sine coefficient on the interval [-L, L] by L A2 = / f(x) sin -L Show…

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Q: (A) Find Laplace transform of the function : f(t)=1 sin(2t+) cos(21-7)

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Q: Question 3: Consider the initial value problem y" - 25y = sin(3t), y(0) = -2, y'(0) = -1. a) [6…

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Q: sin 3at where a is any positive constant and s > a. WHAT IS THE LAPLACE TRANSFORM OF THIS?

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Q: What is the first element of z?

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Q: The complex exponential Fourier coefficients for the periodic function x(t)=t, 0<t<2 is:

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Q: Question 3: Evaluate the Fourier transform of a Gaussian g(x) = ae with a, b>0 %3D

A: Given g(x)=ae-bx ⇒Fg(x)=12π∫-∞∞g(x)e-isx dx Here g(x) is defined for x&gt;0, and  a ,b&gt;0…

Q: Question 7 2s +3 Find the Inverse Laplace Transform of F (s) = s2+4s + 13 A f(t 2sin3t--cos3t 3…

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Q: t - 0.2k æ(t) 2.5 1 – 2 Σ rect 0.1 k=-∞

A: Given that, x(t)=2.51-2∑k=-∞∞rectt-0.2k0.1-12 The aim is to find the complex fourier series, The…

Q: S1 -x, xl 1 Find the Fourier transform off(x) = and hence evaluate sin x) Cos 2 X COS X – dx.

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Q: 1. Choose only and appropriately between the Fourier sine transform and the Fourier cosine transform…

A: Given partial differential equations: ∂u∂t = k∂2u∂x2, x&gt;0ux,0 = fx∂u∂x0,t = 0 To find: The…

Q: Find the inverse Fourier transform of the function 10 sin(3) w+T

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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: 2s + 3 Find the Inverse Laplace Transform of (s+4)3 e" (2cos21+ sin2r) 2 A

A: I am attaching image so that you understand each and every step.

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 +…

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Q: The German mathematician Karl Weierstrass (1815-1897) noticed that the substitution t = tan(x/2)…

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Q: Find the Inverse Laplace Transform of s?+2s + 10 'sin3t A 3 3 sin9 3. cost

A: Inverse Laplace transferom

Q: Question 1: Compute the Fourier transform using the given table for the functions as follows: a) f…

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Q: 7. In the process of computing the inverse Laplace transform of the function F(s) = -23 - arctan ¹…

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Q: Q1. Find the Fourier integral of the given function and discuss it at the discontinuity points…

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Q: Find Fourier Sine and Cosine transform of the function f(x) = e -x

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Q: x2, Ixl a

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Q: Consider the function 0, h(x) = х< -1 = {1 -1<x<1 x 21 Sketch the graph of h, find the Fourier…

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

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Q: QUESTION 2 Find the inverse Laplace transform of 3s+8 F(s) = s2 + 2s+5 O A. e-(3cos(t) + 5sin(t)) B.…

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Q: = sin 2 t, 2 n <t < 4 n and f (t) = 0 otherwise, in terms Represent f(t) of unit step function and…

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Q: x², IxI a

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Q: QUESTION 9 Using the table to find Laplace transform of e'sinh(2t) OA. 3 B. Non of the above. C. 1 O…

A: Recall the following. Lsinhat=as2-a2If Lft=Fs, then Leatf(t)=Fs-a

Q: 4- Find the Fourier sine and cosine transform of: 0 <x < a F(t) = {o otherwise Note: using sin x =…

A: Fourier Sine Transform: Let Fx be defined for x&gt;0. Then Fourier sine transform of Fx is denoted…

Q: 2s +3 Find the Inverse Laplace Transform of (s+4)3 A e(2cos21 + – sin2t) B e-2' (cos2t+ sin21)…

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Q: Find the fourier transform of f(t) = e-2(t+4)ʻ sin (nt).

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Q: (i) cos ax x Find the Hankel transform of (ii) sin ax x

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Q: 1. Find the Laplace transform of the function: f(t) = f(t)= e" coshn(116) -11 Sin3 (E) + I sin (116)…

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Q: ∞ z sin(mz) (1+z²) 5. Find the Fourier sine transform of e- and hence evaluate f dz, m>0

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Q: Find the complex Fourier series coefficients for the signal x(t)= (sin(nwot))5

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Q: S sin a, 0 2. Q.6 (a) Find the Fourier cosine transform of f(r) 0,

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Q: sin

A: We will compare with the standard expression for Fourier series.