DEFINITION 7.1.1 Laplace Transform Let f be a function defined for t 2 0. Then the integral 00 Rf(t)} e-strt) Jo %3D dt is said to be the Laplace transform of f, provided that the integral converges. Find Af(t)}. (Write your answer as a function of s.) (6, 0 4 BAf(t)} (s > 0)

Q: Calculate the inverse Fourier transform of the function, At) if F(@)= 200(jw+1) jw(jw+10)(2jw+4)

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Q: Use appropriate algebra and Theorem 7.2.1 to find the given inverse Laplace transform. (Write your…

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Q: Get the function in algebraic form, state its representation in terms of the function unit step and…

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

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Q: L[2t2 + 5 – 3 cos nt), t > 0

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Q: Check that the Fourier transform of: is g(t) f(w) = { 0 = sin at t -a<w<a rest

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Q: The Laplace transform of L(sin7t) is IS (s? + 7) (s? + 72) 7. (s2 - 72)

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A: To find inverse Fourier transform of Fw=-46+iw3 , we can use some standard Fourier transform…

Q: ansform Prove th

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Q: Equation: Answer:

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Q: f(t): = tan(-7t) cos(-7t) + sin (−8t) e -3t cosh (-4t), 1 + 5 7 +=t5 + sinh (6t)

A: The given problem is to find the Laplace transform of the given function f(t).

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

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Q: Given 30<t ₹2 10 elsewhere find Fw), the Fourier transform of ƒ(t). Compute the values of F(0), F(1)…

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Q: 4. Determine the Fourier transform of the given function: 1 (t) = {2t - t, 2t - 1, 0 < t < 1 0<t<2…

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Q: Laplace transform of ramp function f(t)-DAt is

A: Given f(t)=At

Q: Find the inverse Laplace transform C-{F(s)} of the function 8 F(s) (s – 5)³ NOTE: The answer shouid…

A: Given that, F(s)=8(s-5)3 The Inverse Laplace Transform of the function is determined as shown below.…

Q: use the laplace transform to solve the following IVP x' (+) + x (+) = f (+) x(0)=0 1 where O te[1,2)…

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Q: H(s) = 1 s³ +bs² (use integral rule)

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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: 14. Find the inverse Laplace transform of 2s+1 a) F(s) s²+25

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

Q: By the definition of Laplace transform find the Laplace transfonn of the following functions (a)…

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Q: Determine an inverse Laplace transform of the function. [2] a) 4s b) 2/54 +

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Q: Find the Laplace transform F(s) = L{f(t)} of the function f(t) = 8th(t - 7), defined on the interval…

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Q: Apply the translation theorem to find the inverse Laplace transform of the following function. 6s +9…

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Q: If F(w) is the Fourier transform of f(t), then the Fourier transform of g(t) = -e3it f(t) may be…

A: Here, gt=-e3jtft

Q: Find the Fourier Transforms of the indicated function: f (x) = xe-|x|

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Q: Find the inverse Laplace transform f(t) = L¹{F(s)} of the function F(s) = = f(t) = L -- {7+5)-1…

A: Solution:-

Q: Determine the Fourier transform of the function f(t) = e-cltl.

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Q: Find the Laplace transform F(s) = L {f(t)} of the function f(t) = 3e-10t + 9t + 5et, defined for t >…

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Q: estion * he Laplace transform of f (t) = t2 U(t - 3) is: F(s) = e -35 F(s) = e +.

A: Laplace Transform

Q: Use appropriate algebra and Theorem 7.2.1 to find the given inverse Laplace transform. (Write your…

A: We will find out the required value.