5. Find the Laplace transform of the equation f" (t) + f(t) = sin bt where f(0) and f'(0) = 0 (a ) F(s) = b / [(1 + s?)(s² + b²)] (b) F(s) = b/ [(1 + s?)(s² - b?)] ( c) F(s) = b/ [(1 - s?)(s² + b?)] (d) F(s) = s / [(1 - s²)(s² + b²)]

Q: Ex. Find the Laplace transform for the functions 1-f (t) = sin't %3D 2-f (t) =t°e"

A: We have to use Laplace standard transformations.

Q: Find the inverse Laplace transform of the function as + b H(s) = (s – a)2 + 32 °

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

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Q: 4] Find the Laplace Transform of f(t) = { S-1 (-/= + 5 = /₁1) (1te - 1/₁1) (a) (c) S S - I (b) (d) S…

A:

Q: find the Fourier transform f(x) = e ¹² cos fx|

A: What is Fourier Transformation: A mathematical transformation known as the Fourier transform…

Q: Find F(t) such that F'(t) = sec³ (t) tan³ (t) and F (3) = 0.

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Q: Find the derivative of f(w)= sin(4w²)+cos(4w²). A) Swcos(4w°)–8wsin(4w²) B) -8wcos(4w?)+8wsin(4w²)…

A: Given function is  f(w)=sin(4w2)+cos(4w2)Derivative of f with respect to w:f'(w)=…

Q: Use convolution and Laplace transform to evaluate y''+y=sin(t) , y(0)=1 , y'(0)=-1

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Q: cosh r – 1 · (xª4 + 2) +2). Compute the derivative of y = In | (2x + 1)

A: Given problem:-

Q: Derive the Fourier transform for f(t) = te2t for t>0 and 0 for t<0.

A: The Fourier transform of the function f(t) is represented as F(k), it is defined as ∫-∞∞e-iktf(t)dt,…

Q: w. Determine the fourth derivative of f (w) = 7sin() + cos (1 – 2w)

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Q: 6. a) Find the Fouriér Transform of f(x) = 1-x² (x) 1), b) Evaluate, - I Cosx-sinx cosdx

A: We have to solve the given problem using Fourier transform.

Q: Calculate the derivative of t2 -k 3 - t F(t) = cos(t) i + 3e2t+2j + |

A:

Q: Obtain the Fourier transform of the function where f(x) = 0 for x &lt; 0 and f(x) = e−axsin(bx) for…

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Q: -Obtain the Fourier transform of f(t): = sin (30) -t²+7it+12

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Q: Q3) Verify that the Fourier transform of the function [1–|x|, 1-|x|, |x|1 ƒ (x) = = { 1 + 0 is ƒ…

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Q: Use differentiation in time domain to solve the the Laplace transform: y"+7y'+12y=21e³t; y(0)=7/2,…

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Q: Determine the Fourier transform and plot the magnitude S1, It| < T/2 l0, otherwise (ii) x(t) = f(x)…

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Q: Find the Laplace transform F(s) = f(t)= (3-t) (h(t-4)-h(t-6)), for a 0. F(8) = C {f(t)} 2h(3-1)/s^2…

A: We know for a function g(t),           L{g(t)h(t - c)} = e-cs L{g(t + c)} Here, h(t - c) is…

Q: Prove that the Fourier transforım of f' (x), the derivative of f (x) is – ip f (p), where S(p) is…

A: Answer: For the given data,

Q: Approximate f' (1) using the given data f(0) = 1, f(1) = 2, f(2) = 1, and f(3) = 10 and the Lagrange…

A: Lagrange inteerpolation is used to find a polynomial equation which passes through the given set of…

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: y(4) – y = sin ht

A: