FIND THE LAPLACE TRANSFORM OF y(t) IF ALL THE INITIAL CONDITIONS ARE 'ZERO’. d²y(t) dy(t) dt2 + 6 + 8y(t) = 5. sin(3t) dt

Q: use laplace transform to solve y'-y=2cos(t), y(0) = 4

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Q: Find the Laplace transform of f(t) t sin(2t) dr F(s) =

A: We use the table of Laplace transform to solve the given question.

Q: dy = et. dt Find the solution when y(0)=2 using the method of Laplace transform

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Q: f (1) = = cos 21 + 7 sin 2t s2 + 4 14 s2 +4 s+14 s2 + 14 s+14 s2 +4

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Q: Find the inverse Laplace transform of F (s) 4 F(s) = s²+12 s+52 a. f(t) = e-6 (6 sen(4 t)+cos(4 t)…

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Q: Find the Fourier transform of S (x) =!-\,| sin x dx Hence evaluate

A: Given,    f(x)= 1-x, x≤10        , x>1

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

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Q: 3t y" - y' - 6y = t²e³t - 4t², y(0) = 0, y' (0) = -1

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Q: Use Laplace transform technique to solve y +2y +2y= e-, y(0) = - 4, y'(0) = - 2

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Q: F(t)= t2 sin2t u(t)   F(s)= ?   laplace transform

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

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Q: 4 7 n=1

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Q: Solve using Laplace Transform f(t) = (d2/dt2)(te-t)

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Q: Find the Laplace transform of f(t) = te-5t.

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Q: Solve equation using Laplace transform ÿ +9y = 6 (t -) sin(t), y(0) = 0, y(0) = 0 %3D

A: Given the given equation is y"+9y=δt-π6sint,     y0=0,  y'0=0 Use the property of delta function.…

Q: Determine the Fourier transform of f(t) = te-2t u(t), where

A: Given ft = te-2tut where ut =0     t<01    t>0 The Fourier transformation is given by Fw…

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: f(t) = [1– uzn(t)](2 sin t – sin 2t

A: Solution

Q: Please help me find the laplace transform of the following equation: 0.00174y''+0.295y'+25y=200u(t)…

A: If Ys is Laplace transform of yt. Then Laplace transform of y' and y'' when y(0)=0, y'(0)=0 is sYs…

Q: d2y/dt2+a2y=b sin wt  ( laplace transform )

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Q: (3) A signal has Fourier transform as, 1 sinc (2w X(w) sinc + 2. Compute x(t)

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Q: 1. Find the forier tansform of f(t) = 8(t) + 2e-3lt| %3D

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

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

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Q: whatarecenonical transfor mation their advastagez Prove and is the following relation for function…

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Q: у" + 2y'— Зу%3D бе 3t У (0) — 0, у' (0) - 0 %3D

A: Here we use simple Laplace transform to solve this