S1 -x, xl <1 0, x| > 1 Find the Fourier transform off(x) = and hence evaluate sin x) Cos 2 X COS X – dx.

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 inverse Laplace transform of F (s) = 3 s²+1 O 3 cos t O sin(3t) O cos(3t) O 3 sin t

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Q: e-2t cos 3t cOS

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

Q: 3. f(t) = t°e^(-4t) 4. f(t) = (e^(10t)) sin(2t)

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Q: 2b. Determine the solution of the following problem using the concept of derivative and integral…

A: The given problem is to find the Laplace transform of the given integral term function.

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

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Q: Using Laplace transform to solve y' +y = sin(t), y(0) = 1.

A: Applying Laplace transformation,

Q: 2. Use Laplace transform to solve y" + y = 8(t – 27) cos(t) y(0) = 0, y(0) = 1

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Q: Q4 a) 0, if x 0 1,0 < x < 1 x ≥ 1 b) Evaluate Fourier sine transform of f(x) = {¹,0

A: (a) We have to evaluate Fourier integral representation of the given function. f(x)=0if x&lt;012if…

Q: -4 Inverse Laplace transform of is given by s2-16 sinh(-4t) O sinh(4t) O cosh(4t) O cos(-4t)

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Q: Solve the equation dy y ху-з dx II +

A: The given equation is of the bernoulli's equation form.

Q: a) Solve the initial value problem using Laplace transform I UTM UTM 26 sin 3t, y(0) = 3. UTM

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Q: -kx (b) Find the Fourier integral of the function f(x) = e when x > 0 and f(-x) = f(x) for k>0 cos2x…

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Q: 3. Using Laplace Transform Solve d'y dy = sint, given that y =! dy =0 when t=0 +2 - 3y dr? dt dt

A: The given problem is to solve the given initial value problem with given initial conditions using…

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: -4 Inverse Laplace transform of is given by s2+16 O sinh(4t) O cosh(4t) O cos(-4t) O sin(-4t)

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Q: (i) Find L(cos(at + b)] where a and b are constants. (ii) Using Laplace transform, evaluate fote-³t…

A: Disclaimer:  Since you have asked multiple question, we will solve the first question for you. If…

Q: S Prove using the definition of laplace transform: L(cos 3t) s2+9

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Q: Q8 Find the Fourier transform: of: sin f - pn Sx< pm f(x) = otherwise Take p = 4

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

Q: Solve for the laplace transform x(t) = (t+3) sin(t-6)

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Q: 4. If f(x): = cos Tx then the Laplace transform L{f(x)} fthe differential couation(v -x)dx + 2ydy =…

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Q: i) Obtain the complete and singular integrals of : = px+qy+ pq . -3t ii) Find the Laplace transform…

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Q: What is the first element of z?

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Q: Use the Laplace Transform to solve the initial value problem. Show your work. y" – y - 2y = 5 sin x;…

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Q: Find the Laplace Transform of f (x) = 2 sin a + 3 cos 2x. %3D Answer: 3s a. 2+1· $2+4 3s b. - s2 +1…

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Q: 10) Use the Laplace transform to solve the given initial-value problem. y'-y = 2 cos (3t) when y(0)…

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Q: using Laplace transform, solve the equation below. y'' -2y' + 2y = cos (t)         y(0) = 1,  y'(0)…

A: To find the solution of differential equation we use the properties of Laplace transform of…

Q: (0, 0 b asxsy

A: Fourier Transform

Q: a"(t) + 16x(t) = 5 sin t, a'(0) = x(0) = 0 %3D

A: First we have to take Laplace transform of the given equation.

Q: || > 1 {e*cos(x), x|< 1 30. f(x) = {0, %3D Does this function have a Fourier transform (i.e., does…

A: Given fx=excosx, x&lt;1. As it is known that Fourier Transform of fx exists if the function is…

Q: Find Lf" sin /6t-r'e"}

A: Please see below

Q: 3s+1 F(s) = s2 +4

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Q: Q1) using Fourier transform find x(t) below x(t) = [e-3tu(t) * e-6*u(t)] dt

A: Solution is given below

Q: Using Laplace transform, sole cỳ"+y= cos x, where y (0) = 0 = y'(0)

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Q: b) By applying the definition of Laplace Transform, find the Laplace transform for f(t) = cos 3t.…

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Q: (i) Find the Laplace transform of e" sin 21 dt (ii) Form the PDE by eliminating arbitrary constants…

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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: 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: x2, Ixl a

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Q: Find Laplace transform of the function: f(1) = sin 21(et cosh 41+ cos(x + 1))+1(2 cos 31+1'e¹) 11.00

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Q: Using Laplace transform, solve y" +y = cos x, where y (0) = 0 = y'(0).

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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: Inverse Laplace transform for 6s (s+ 1)(s+2)(s+4) is

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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: 8. Using the Laplace transform, find the solution to y" + y = sin t, y(0) =0, y'(0) = -1. %3D

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Q: y"+ 4y' = cos(t - 3) + 4t, y(3) = 0, y'(3) = 7

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Q: 4. Solve using the Laplace transform: y' + 2y = cos 3t , y(0) = 4.

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Q: The first: find using transform i x =rcos(0), y=rsin(0) 00 00 e-(7x²+3y) dxdy

A: We have to use the given substitution.

Q: 4. Use Laplace transform technique to solve , y"+2y'+2y = e given y(0) = -2 and y'(0) =-1 %3D

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Q: 54. If Fe (n) is the Fourier cosine transform of f (x) on 0 < x < 1, show that Fel8" (=)) = }(-1)"…

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