1. The Laplace transform of a function f(t) is given by the express F(s) = L{s(t)}- jst*dt %3D %3D 0. Find the Laplace transform of the following functions: f(t) = t(e-2t + cos at) %3D а.

Q: f (t) = 2e¬ + 4 sin t cos t %3D

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Q: A function f(t) is given as f(t) = e' cos 2t cos t %3! Find the Laplace transform of this function.

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Q: cos x, 0 a

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Q: f(t) = [1 – u2m (t)](2 sin t – sin 2t)

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Q: Find the Laplace transform of f(t) = cos(2t) * u

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Q: (a) Find the Laplace transform of the function: f(t) =e-$' t3/2 (b) Find the Laplace transform of…

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Q: B. Find the Laplace transform of f(t) = e-²t fsint dt

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Q: cos x, 0a

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Q: (ii): f(t) = sin (t + 7)+ e³' cosh 5t

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Q: f(t) = [1– u2m(t)](2 sin t – sin 2t) U2n

A: Some of the properties of Laplace transformation Lsinat=as2+a2Luc(t)=e-cssLuc(t)g(t)=e-csL[g(t+c)]

Q: Find the Laplace Transform of (i) e3(2cos 5t - 3sin 5t) (ii) e2tcos² t 4t (iii) e**sin 2t cos t

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Q: Let F(s) be the Laplace transform of f(t) = cos (k(t – 7)] e" sin(37)dr, where k is a positive…

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Q: Find the Laplace transform of the function f(t) = u₁(t) + 5u6(t) — 4u5(t) The Laplace transform F(s)…

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Q: 1.a Find the Laplace transform of the function F(t) = e-2t (cosh 3t + sinh 5t)

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Q: 2. ts) Use the table of Laplace Transforms and 1st shifting theorem to find the Laplace transform of…

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Q: Q5) Find the Fourier transform of: SCos(nt/t) for lel < x(t)=D .elsewhere) Sketch X(f) versus f.On…

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Q: 5 The inverse Laplace transform of F(s) = 5² - 2s+5 1 f(t) = 5e²¹ sin 2t f(t) = 5e¹ sin 2t 5 f(t) =…

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Q: Find the Laplace Transform A- f)=tcos(@r) B- f(1)=tsin(@t) C- f(t)=tcosh(at)

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Q: Determine the Laplace transform of the function. a) [4+sin(31)+5e²]- b) Z[6r'+2t’e" +sinh(4)].

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Q: orm y(t) = 4e-2cos

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Q: Exercise 1. A student is asked to prove If m is even and n is odd, then m² + n² is odd. 2 The…

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Q: ®[6.4] Using the Laplace transform to solve IVP. yu t16y= 43(t-37) H10)=2 , y'0) =0 y10)%=D2 %3D 3D0

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Q: Find the Laplace transform for 1 (a) f(t) = sin? t J 3) (b) f(t) = e-4t sin 3t (c) f(t) = t sinh 5t

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Q: Find Fourier Transform for the function:f (t) = sint - T <t< %3D

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