f(t) = {t, 0

Q: y Ct) = 5e - 2t Cos 67 fCt) = 3c 4t C1- 3t + 2t 2) -4t (1- 3t + 2t²)

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Q: Find the Laplace transform of the function

A: The Laplace transform of the function is represented as or , it is defined as , since the…

Q: Problem 8 Write the function if 0 2. in terms of unit step function and find L (f).

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Q: Find the Laplace Transforms of the function

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Q: 216 X(s) = s4+5s3+15s2+45s+54 2s-9 Y(s): s(s2+10s+146)

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Q: c) Find the inverse Laplace transformation of the function given by 2(s+3) G(s) = s(s²+2s+5) *

A: The posted question has multiple questions but according to guidelines we will solve the first…

Q: 4 (iv) F(s) = s2 +9 2s + 16 (v) F(s) : s2 + 4s + 20 3s – 15 (vi) F(s) %3D 2s2 – 4s + 10

A: The Laplace transform of a function is an integral that converts the real variable into complex…

Q: s2-2s 4. F(s) = s4+5s2+4

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Q: f (t) = t5 e(1-t)

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Q: co sh?Ł

A: As we know,    cosht = exp(t)+exp(-t)2                  and               Laplace transform of ept =…

Q: 2ct-3) cos Cも-3) yct) = sin 2t cos 3t

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Q: L{e' sinh(t)}

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Q: π od T = ¹. Ans: V a

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Q: 3s+5 F(s) s2-6s+25

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Q: 2. x(t) = e5t + cos 3t %3D

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Q: e at -e bt

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Q: Find the Laplace transform

A: Given,

Q: Evaluate the Inverse Laplace transformation of the following functions

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Q: Find the Laplace Transformation of y" +3y' +2y= 4e* when y (0) = 0, y (0) = 3 OY (s) = 2s +1 2+252s…

A: The formula for y' and y" in terms of Laplace transform is given by Ly"=s2Ly-sy0-y'0 and Ly'=sLy-y0…

Q: (t – 1)* 24 24 12 4 1 24 24 12 4. O option 2 Option 1 24 - 24s- 12s2+ 4s° + s4 24 - 24s +12s2- 4s +…

A: Using Laplace Transform to Evaluate the Function (t-1)^4

Q: 3. x(t) = 3t7 + 8

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Q: a) f(t) = t¯/2 b) f(t) = t\/2 c) f(t) = t32. %3D %3D

A: To find the Laplace transform of the given functions using the definition of Gamma function.

Q: {t²,00 (t²,0 ≤t≤2 0,t> 2 Sketch f(t) = - and find L{f(t)}

A: Sol

Q: 1. x(t) = 3t5

A: Given Function: x(t)=3t5 constant multiplication property of Laplace Transform:…

Q: 1. L{e*t³} Ans. 2. L{ e-5t cosh 4t}

A: using laplace formula and shift theorem...