e-2t cos 3t cOS

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: L{t + et} =+ I. L{t + e3t} = = 1 %3D II. S-3 52 5-3 L{t + e*} =+ L{t + e#} = - III. IV. S+3 52 543

A:

Q: y" + 4y' + 4y = 2e, y (0) = 2, y (0) = %3D %3D

A:

Q: 2. F(s): = 3s² +5s-4 S4

A:

Q: 2e-2s 22. F(s) = s2 – 4

A:

Q: 5. t²e-2t sin 4t

A:

Q: 3. 6 сos(4t — 1)

A: The solution is given as

Q: How is the existence of the Laplace transform of a function guaranteed?

A: We known that the  Existence of the Laplace transform of a function guaranteed

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

A:

Q: e at -e bt

A:

Q: Find the Laplace transform

A: Given,

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: 3. Find the inverse Laplace Transform of the g

A:

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

A:

Q: Find the Laplace transforms F(s) of the following functions: a. 4t+3 b. 5e²¹ +4e-3t c. 3t² +8 sin 5t

A:

Q: (2,0 st 3

A:

Q: -3t cosh 2t

A:

Q: How do you write the Laplace transform of this translated Heaviside function?

A: Given - ft = 0x < π1x ≥ π To find - Write the Laplace transform of given translated Heaviside…

Q: cos(2t + 30°)

A:

Q: 51²e-31 – e121 cos 8t 10 (s+3) 3-12 (১-12)-64 10 s-12 ((-122+64 (s+32 10 (s+32 s-12 (-127-64 10 s-12…

A: lets see the formulas we are going to use here L{ tneat } =n!(s-a)n+1               ⋯⋯⋯(i)L{ e-at }…

Q: F(t) = 2T, 0 < t <3; F(t+ 3)u(t – -

A:

Q: 1. x(t) = 3t5

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