Find the Laplace transformation of the following: 1) (2t² – 1)2 2) cos³t 3) sinh³t Hint: sin CoS

Q: 3. Evaluate Laplace transform to + 5 sin7t . 3 2

A: We have to find the Laplace transform .

Q: f(t) = 3e7t - 3 cos(3t) + t?e-4t + 6.

A: Given  f(t) = 3e7t - 3cos(3t) + t2e-4t + 6    Results:  1) Laplace transformation is linear  2)…

Q: Find the Laplace transform of the following: 1. y" + 2y' + 5y = t cos(5t) - 6, y(0) = 1, y'(0) = -2

A: To find the Laplace transform of the problem.

Q: 1.) f(t) = (cos3t – te2t)²

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Q: 5- Fit)= b Uct-a) -2b4lt-29) + bu(t-34) %3D Laplace transform

A: The detailed solution is as follows below:

Q: Given that L{cos bt}(s) = s². Click here to view the table of properties of Laplace transforms. Le…

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Q: B: Find Laplace Transform of f(t)= cos3t By DEF.

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Q: Find the Laplace transforms of the following. r -6t sinh(2t) 1. -6t cosh(2t).

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Q: 2. Find the Laplace Transforms of (te' sin(at))" when a = 1

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Q: 6. Find the Laplace transformation of the following functions (b) f (t) = }e-15t + cos 8t

A: It is given that  ft=23e-15t+74cos 8t   Since we have, Le-at=1s+aLcos at=ss2+a2

Q: Given that L{cos bt}(s) = s2 + b2 use the translation property to compute £{e at cos bt}. Click here…

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Q: Use the Laplace transformation to solve the problem: x >0, t>0 %3D 2

A: In this question, we have to solve the Laplace equation by using Laplace transformation. the wave…

Q: Find the Laplace transforms of the .given functions f(t) = cos (5t)

A: using trigonometric identites : cos (2t) = 2 cos2(t) - 1rearranging we have cos2(t) =cos(2t) +…

Q: L{e2"sin2t + etcos3t}

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Q: 1. solve the following different equation using Laplace transformation: dry dat -4 d2 +67 = 4€ 4t;…

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Q: Solve the given by using the Laplace transformation.   L[7t^4 + 4 cosh(2t) + 5e^3t + 2 sin(4t) ]

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Q: -8e4t* + 2e6t cos 2t

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Q: B- Find Laplace transformation for the following 1. f (t) = sin3t 5. g(t) = {(t %3D

A: Since you have sent multiple questions therefore according to our guidelines we can answer just one…

Q: π od T = ¹. Ans: V a

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Q: 11. te- cos(3t) cos (3.

A: As per our guideline we are supposed to answer only one asked question. Kindly repost other…

Q: S , use the translation property to compute eat cos bt). *** Given that cos bt)(s) = s². Click here…

A: The translation property is: Leatft=Fs-a

Q: 8 4t3e-2t + 2 cos 4t

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Q: Find the Laplace transform of the following: 1. 4t + 12 2. 1.5 sin(3t-3)

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Q: Determine the Laplace transforms of the following functions. (a) 3e-4t - 5e4t (b) sin 4t + cos 4t…

A: Dear student, According to our guidelines we can answer only three subparts of the questions.

Q: B/ Find the Laplace transforms L[ 2sinh 5t + 8 cos h 3t]

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Q: Solve the following IVP using Laplace Transformation 7. y' +2y =0, y(0) =1, y'(0) = 4

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Q: find laplace Transforms fct) = I+ 7t sin h2t %3D

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Q: Find Laplace transformation for the following f(t) = -2t + ez cosht %3D

A: Answer

Q: 6. Find the Laplace transformation of the following functions: (a) f(t) = 2e-3t + 5t4 – 3 sin 2t

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Q: Find L T Cos(37)dt 0,

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Q: Find the Laplace transforms of the functions. f(t) = Cos^2(2t)

A: Let ft=cos22tTo find: Laplace transform of the function ft.

Q: Find the Laplace transforms of f(t) = e(3t-7) cos3(6t).

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Q: 1. Find the Laplace transformation of function f(t)= e-2t +sin(t-2) + t²e-3t

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Q: s+ 8 F(s) %3D s2 + 16s + 68

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Q: 6. Find the Laplace transformation of the following functions: (b) f(t) = e"(t? + cos 3t)

A: Given function; f(t) = e2t (t2 + cos3t)

Q: L{(1+te*)³}

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Q: 1. t?cos2t 2. tsinh4t

A: Use the property of Laplace transform Ltnf(t)=-1ndndsn L f(t)  . Use the formulae of Laplace…

Q: Find the Laplace Transformations of the following functions i. L{(sin t + cost)² - cos² 3t}…

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Q: -St Find aG 2t? t te

A: As per the instruction, we will answer only the first one. So,…

Q: L[(2ピ-tt)u(t+>]

A: TO DO

Q: 3e CoshC4e) 36 3. +2)

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Q: Determine the Laplace Transform of the following: 1. te-3t + tcos2t + e-3tcos2t 2. te-3'cos22t 3.…

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Q: we are asked to solve using laplace transformation, the given is y'''+3y''+3y'+y=30x^2e^x

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Q: Calculate the laplace transforms by using laplace taeafor Pairs/tables 1. Ft)=10+8t. 2. f(t)= exp…

A: Solution by using table of Laplace transform as follows :

Q: t2, 0 2

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Q: f (t) = (2at -3t b. cos ( 3at + COS +

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Q: Determine the following Laplace transforms: i) L cosh at) i) -35+9 iii) Ls +5 7-23+1 2s+1 iv) Ls+…

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Q: Find the laplace transformation of the following 3x' +34 + 5X = 25 Cost X(0) = 2 ノ 2x` - 33' = 5…

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Q: Find the laplace transform of f (t) = 2t1 – 3et + 10 cos 2t %3D

A: We will use property and tables of laplace transformation

Q: ) Find the Laplace Transformations of the following functions L{e-t sin 3t+4e-t cos 3t}.

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