Find the Fourier transform specified in part (a) and then use it to answer parn (b). (a) Find the Fourier transform of e-" sin pt t>0, t< 0, f(7. p.t) where y (> 0) and p are constant parameters. (b) The current I(t) flowing through a certain system is related to the applied voltage V(t) by the equation I(t) =K(t-u)V(u) du, where K(t) = af(y1, P1, 7) + azf(72, P2, T). The function f(y, p, t) is as given in (a) and all the a, n (> 0) and p, are fixed parameters. By considering the Fourier transform of I (t), find the relationship that must hold between a, and az if the total net charge Q passed through the system (over a very long time) is to be zero for an arbitrary applied voltage.

Q: e-2t cos 3t cOS

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

Q: Find Fourier transform of i 1x ka f(x) = 1₁ 0 Ixl ya Then find: 05- Sin Pa Cospx dp , P of M.H sin…

A: Fourier transform of the function and deduce the given definite Integral

Q: Find the Fourier Sine Transform of e-t and hence find the Fourier Cosine Transform of te-t.

A: Fourier sine transform of e-t is ∫0∞e-tsinωtdt. Calculate it:  ∫0∞e-tsinωtdt=∫0∞e-teiωt-e-iωt2idt…

Q: (11) The Fourier cosine transform of the function f(x) e; x>0, is

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Q: A uniformly stretched string and fastened to two points 10 meters apart. The displacement of the…

A: The solution of the given wave equation which satisfies the boundary conditions is given as, and…

Q: 1 The Fourier transform of [e 2 x(t + )] is jt 1 jn( f- X(f)e#ft X(f – e"(s-±) 4 t A. O . A.…

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Q: 2. Calculate the Laplace transform L{12e cos²(3t)}.

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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: 2Ct-3) Cos Ct-3)

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Q: 8.(a) Find the Fourier transform for the function cos x, -n/2 7/2 f(x) = 0, (b) Use the result in…

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Q: 4) Find the Fourier transform (FT) of the rectangular pulse signal x(t) analytically by using FT…

A: Find the Fourier transform (FT) of the rectangular pulse signal x(t) analytically by using FT pairs…

Q: A 4-pound weight stretches a spring 2 feet. The weight is released from rest 18 inches above the…

A: A 4-pound weight stretches a spring 2 feet. The weight is released from rest 18 inches above the…

Q: 1. a. Write the Fourier series for a rectified wave for which half is defined by f(t) = sin(t),0 <t…

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Q: Find the Laplace transform of 4 sin(3t)+2 cos(9t).

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

Q: 3. Find the Fourier Transform of a t < 2 a а f(t) = 1 %3D -- 2 < t Whose graph is shown below V t. V

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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: 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: e2t+a (2 cos at – 3 cosh 2at) -

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Q: Find the fourier sine transform of a) f(x) = exp(-ar) and deduce sin(sz) -ds = 2+a² -az b) f(x)= re'…

A: Consider the provided question, Hello. Since your question has multiple parts, we will solve first…

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

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Q: of the function. 4. Find the Fourier transform of of 1/(1+t²).

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Q: 4. e2t+a(2 cos at – 3 cosh 2at) -

A: It is given that the function ft=e2t+a2cosat-3cosh2at. We have to find the Laplace transform of ft…

Q: Find the fourier transform of following signals a. x() = cos (2xf.1) b. x(1) = sin (27f 1) c. For…

A: Calculate Fourier transform of cos22πfct: Fcos22πfct=F122cos22πfct-1+1…

Q: Find the Fourier transform specified in part (a) and then use it to answer part (b). (a) Find the…

A: In part (a) we have to find the Fourier transformation, Given, f(γ,p,t)=e-γtsin pt  t&gt;0,0…

Q: 2. Find the Laplace Transform of the following differential Equations. a. cos't

A: Find your answer below

Q: 9. Find the fourier series of a. f(t) = {* sin ny+t, 0<t<n 0, -4 <t<0 nsts 2n h. f(t) = St, -6t,…

A: Note:- according to the company policy we can attempt ?️ only one question so please upload the next…

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: 1. (a) Given the Z-transform of sinwt and coswt, find the Z-transform of -at sinwt and e-at coswt by…

A: Introduction: Z transformation follows many different properties. These properties are widely used…

Q: 1. Find the Fourier series coefficients for the following signals: a. x(t) = sin(4t ) + 8+3 cos(2t +…

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Q: Find the Fourier transform of f (x) defined bv f x) = , a 10, > a and hence evaluate sin pa cos dp…

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Q: Solve the Laplace transform of: 3 cos 8t + 2 sin 8t

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Q: Determine the fourier series representation for the signal f (t) = e* sin (25

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Q: Q6) A-Show that: a) X(f)=X*(-f) 4 To/2 b) if x(t) is even, then b=0, ano/²x(t) cos(2πnfot) dt…

A: Solution : A) a) X(f)=∫-∞∞x(t)e-jftdt X*(f)=∫-∞∞x(t)e-jftdt* X*(f)=∫-∞∞x*(t)ejftdt…

Q: [a² - x², Find the Fourier transform of f(x)= • 0, and hence 1C. |x| > a evaluate (Sin sint-t cost…

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Q: x2, Ixl a

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Q: A 4-pound weight stretches a spring 2 feet. The weight is released from rest 20 inches above the…

A: Find the equation of motion. Here y(t)=x(t)

Q: 2. Find L{e3t cos 2t} using property of Laplace transform

A: We’ll answer the first question (Question number 2) since the exact one wasn’t specified. Please…

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

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

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Q: a Find the Fourier transform of the signal x(7) = 2 cos(m)[(1+3)-(1-3)], using the Fourier integral.

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Q: -6t-8 Calculate the Laplace transform L{f} of the function f(t) = e 7t – 6 cos(5t) + 3 using the…

A: We solve this by using Laplace Transform

Q: 1. Find the Fourier transform of the function h(t) 4 -+ 2e-nt2 - ei4nt

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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: 1 (iv) If f(t) = e2ºH(t), its Fourier transform is F(@) = -2+iw

A: In this question we have to find whether it is true or false.

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

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Q: A 4-pound weight stretches a spring 2 feet. The weight is released from rest 15 inches above the…

A: Given m=4 lbs=2 feetAnd also, damping constantβ=78x(0)=1512 feetx(0)=54x'(0)=0

Q: sin

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