Question 8: (₁²+1 Let f(t) = 5 1²/² + 1/²/² Find the Laplace transform 2|32| 0 ≤t π

Q: A function f (t) = e-at is defined for a > 0 andt > 0. By finding the Fourier transform show that…

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Q: Find the Laplace transform of f (t) = t 2 7-t 0 if 0 7

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Q: Find the Fourier transform 1-x, | x | 1 sin x Cos X CoS x Hence evaluate dx.

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Q: Find the Laplace transform, if it exists, of each of the following functions f(t)= {e-2x (5 sin2x -…

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Q: A) Find x{(e-51-7)²} L B)[ Use the definition to evaluate the Laplace Transform of the function 2,…

A: FIRSTLY WE USE AN IDENTITY, a-b2=a2+b2-2ab ⇒e-5t-72=e-5t2+72-14e-5t⇒e-5t-72=e-10t+49-14e-5t AND THE…

Q: 6. Find the inverse Laplace transform of the following functions. a) F(s) = ln (5+3). UTMUT TM UTM…

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Q: Obtain the inverse Fourier transform of TU F(w) = {cos (4w) if |w| < 4 0

A: The given problem is to find the inverse fourier transform for the given function F(w).Given F(w) =…

Q: Find the inverse Laplace transform L-¹{F(s)} of the function F(s): L-¹{F(s)} = = 2 s²+7s 8 NOTE: The…

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Q: Find f(x) = f a-1x1 0 the Fourier a-1x1, Hence prove transform Ixl <a , Ixla that 1 (sin t t 0 2 of…

A: Given f(x)=a-x,x&lt;a i.e., -a&lt;x&lt;a                   =0,         x&gt;a i.e., x&gt;a, x&lt;-a…

Q: 5 - Calculate the Fourier transform of 100 – 5t 0 <t< 20 f(t) = otherwise

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Q: QUESTION 1 Calculate the Fourier transform of f(x)=√√ex and evaluate f(0) = f (w) denotes the…

A: Ans: 2 1 1 For detail...go through the solution...I have done in detail

Q: Q2) Find the Z transform X(z) of the following function X(t) 5 – 3e-2t for T=1 sec. and k 20

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Q: Find the inverse Laplace transform L¯¹{F(s)} of the function F(s) L-¹{F(s)} = = 6 (s − 1)³ NOTE: The…

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Q: Sketch the function below, express it in terms of window and step functions, and compu its Laplace…

A: A function gt=t0&lt;t&lt;22cost-22&lt;t&lt;4π+210t-2t&gt;4π+2 To Find : Sketch the given function…

Q: (1-6 (1-5 (1-5)

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Q: n=1 3. Find the Fourier transform of the following: f(t) = {et, -1 < t < 1 otherwise 0, Ans. Ans.…

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Q: 7. L+ Ri = E,where L, R, and E are constants when t = 0, i = 0 t%3D dt

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Q: a. Find Fourier transform for the following function l(x): -1 15 |(x) = {". (Hint: \r| =r for r> 0,…

A: The given function is  l(x)=1 if -1&lt;x&lt;10  if |x|&gt;1 We know that the Fourier transform of a…

Q: 3.3 using the fourier transform, f and g are in the first picture and the question is in the second

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Q: f(x) = x (a? – x?)"-3/2 H(a – x),

A: Given fx=xa2-x2v-3/2Ha-x,  v&gt;1/2, a&gt;0

Q: 4) f(t) = [ Hu(t-IT) Jun (6) fœ

A: Laplace transform of the function

Q: 7. Graph the function f(t)=2U(t-1)-3U(t-2) and find its Laplace Transform 8. Write the function…

A: Remark : As per new guildline,  in case  of posting multiple question we will answer of only first…

Q: Question A) E 2 [ 1: s] Find L {(e-4t-7)²}. B) Use the definition to evaluate the Laplace Transform…

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Q: Find the inverse Laplace transform L-¹{F(s)} of the function 2 F'(s) s² + 5s 6 NOTE: The answer…

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Q: 5.) f(t) = cos (mt) u (7-2)

A: Laplace transform of the function

Q: Use Theorem 7.4.1. THEOREM 7.4.1 Derivatives of Transforms If F(s) = £{f(t)} and n = 1, 2, 3, . . .,…

A: If f(t) is a function of t defined for all positive value of t, then the Laplace transform of the…

Q: Question 1: Find the Fourier transform of f(x) -1 if -1x>0 0 otherwise

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Q: 2T (-1Y- Find f(x) if its finite sine transform is given by f, (p) = where 0<x < T. -, p = 1, 2, 3,…

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Q: d³c(t) dt3 d?c(t) , dc(t) + dt d?r(t) dr(t) + 4- dt + 3r(t) +3- + 5c(t) = dt2 dt2 dc(0)_ d²c(0) c(0)…

A: Applying the laplace transform of the equation.

Q: 4) Find the Laplace Transform of the following functions: f(1) = Lu(t – n) n=0 f (t) = (-1)t/a] *]…

A: a) Given function is , ft=∑n=0∞ut-n     =ut-0+ut-1+ut-2+···· To find : Laplace transform of ft…