Use Definition 7.1.1. DEFINITION 7.1.1 Laplace Transform Let f be a function defined for t 2 0. Then the integral LARE)} = | e-strt) dt is said to be the Laplace transform of f, provided that the integral converge Find {f{t)}. (Write your answer as a function of s.) {Rt)} = (s > 0) f(t) + (2, 2) 1

Q: f(t) = 2sin(bt)sinh(bt)

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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: ∞ -3t Evaluate test sin 3t dt. [Hint: Use the definition of Laplace transform]

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Q: Use appropriate algebra and Theorem 7.2.1 to find the given inverse Laplace transform. (Write your…

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Q: Find Fourier transform for f (t-2)

A: We have to solve given problem:

Q: Find the inverse laplace transform of the followin function FIS) = l0-4s (S-23

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Q: L[t e-t sin 3t dt ]

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Q: -31 19. f(t) =re

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Q: 2s3+ 4s²+1 F(s) = (s²+ 2s+17)(s²+ 4s+20)

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Q: f(t) = eat sin Bt.

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Q: 2s²+7 F(s) (s+1)(s+2)(s²+ 2s+5)

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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: f(t) = cos(2t + 3) + e¬tu(t – 4) + tcosh²2t

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Q: L{t – e-3t} = + s-3 L{t – e-3t} = =-- I. II. s-3 L{t – e-3t} = +3 L{t – e-3t} = III. IV. %3D s+3

A: We know the Laplace transforms Ltn=n!sn+1, s>0 L ea t =1s-a, s>a Now, Lt-e-3t=Lt-Le-3t L t…

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: ssent, if 0n

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Q: Can you provide 2 Examples of Finding Laplace Transform containing t and exponential using the…

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Q: 1. x(t) = 3t5

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