Q1) A: Find the Laplace transform : L{e-3t. sin3t} 1. 2. L{sin²t}

Q: Solve the laplace transform of f(t) = sin3 (10t). Hint: You may convert the given to whichever form…

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Q: Find the Laplace Transform: 2x2 e* cosh x

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Q: What is the Laplace transform of y’’ – 6y’ + 15y = 2 sin (3t), with y(0) = -1 and y’(0) = 4

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Q: Q2: find the laplace transform for the: y = e-*, x.cos2x

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Q: Use the definition of Laplace transform and Euler's formula to find the Laplace transform of cos t…

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Q: 3. What is the Laplace transform of 2sin t + 2cos t ?

A: Given x(t)=2sin2t+2cos2t Now we will find the Laplace transform as shown below

Q: 7. Use the Laplace Transform to solve the IVP y +2y - y -2y= sin(3t) ,y(0) = 0, y'(0) = 0, y'(0) =1

A: We have to use Laplace Transform to solve IVP.

Q: Q1\ Find the Z-transform of A) cosh 2

A: The given question can be solved as shown in step2.

Q: 4. e sin 2t

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Q: 2 sin 4t t

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Q: 2. Calculate the Laplace transform L{12e cos²(3t)}.

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Q: 3 find The Laplace transform f(t) = sint

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Q: Solve for the Laplace transform of f(t) = 5 using long method. %3D

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Q: S Prove using the definition of laplace transform: L(cos 3t) s2+9

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Q: 5. Calculate the Laplace transform L{sin(t - k) - H(t -k)}

A: To find the Laplace transform of

Q: 5) Evaluate te " cos 3tdt using Laplace Transform! -4t

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Q: 3t x(t) = to

A: We have to apply the Laplace transform of the given function.

Q: Find the inverse Laplace transform of -6s e F(s) = s2 + 2s – 3 - - (Use for u.(t) .)

A: The given expression is Fs=e-6ss2+2s-3. We have to find the inverse Laplace transform of function…

Q: Find the Laplace transform of t cosh 2t

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Q: 4. Solve for Laplace transform of f(t) = t^5 using long method

A: This question is based on Laplace transform formula.

Q: Find the Laplace transform of 4 sin(3t)+2 cos(9t).

A: The Laplace transform of the function f(t) is represented as F(s) or L[f(t)], it is defined as…

Q: Using Laplace transform, solve dy a + 6y = 3sin(2t) with y(0) = 1 and determine y(1) in 4 decimal…

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Q: a. Determine the formula for the Laplace transform. et sin 5t-t³ + e 2t) = (Type an expression using…

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Q: 1. f(t) = cos(6t)

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Q: 5 sinh (3t) +4 cosh (3t)

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Q: Solve the Laplace transform. L[ t3sin 2t]

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Q: Laplace transform of sin(5t)u(t) is

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Q: find the Laplace Transform.  1. (et - e-t)2 2. sin2t sin5t 3. e2tcos2t

A: The objective is to compute the Laplace transform of 1. et-e-t22. sin 2t sin 5t3. e2tcos2t

Q: Find the Laplace transform using convolution theorem: Te2" sin(2(t - T))dr.

A: So, here f(t) = sin(2t) and g(t) = t e2t.

Q: y Ct) = 5€ - 2t Cos 6t

A: Use the following 1.L{cos at}=ss2+a22.If L{f(t)}=F(s)Then L{eatf(t)}=F(s-a)

Q: welą Find the inverse Laplace transform of ,-7s F(8): s2 – 1s – 6 f(t) = - (Use step(t-c) for u,

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Q: Find the Laplace Transform of: e-2t sin2t + e3tt2 3t +2

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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: -3t cosh 2t

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Q: sin(2t) cos(2t)

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Q: Starting from the definition of the Laplace transform, calculate: a) L{(cosh(2t)}

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Q: sinh³ 4t

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Q: The Laplace transform of L(sin7t) is

A: We have to find Laplace transform of…

Q: (a) Find the Laplace transform of f(t) = te2" sin(2t). %3D

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Q: What is the Laplace transform of 7sin (6 t) sinh(6 t)

A: What is the Laplace transform of 7sin (6 t) sinh(6 t)

Q: Solve for the Laplace transform of the function 8cos(at) and then solve for the value of a. Show…

A: Topic:- Laplace transform

Q: Find the laplace transform of f (t) = 2t* – 3et + 10 sin 3t

A: The solution is given as

Q: Find the Laplace transform of the following: 1) sinh3 4t

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Q: 1: A :Find Laplace Transform of f(t) = sin²t By Rule.

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Q: Determine the Laplace transform: e2t sin (wt + 6.

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Q: 2. The laplace transform of f(t) = et

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Q: 2. Laplace STO 2 3. What is the Laplace transform of 2cos t?

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Q: (b) Using Laplace transform, evaluate te -2t Cos 2t dt 0.

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Q: 5. * + 9x = cos 2t

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Q: The Laplace transform of L[2 sin 5t sin 4t] is

A: Laplace transform can be solved by using trigonometric identities and Laplace transform of…