. Using a hand calculation, find the Laplace transform of: f(1) = 0.0075 – 0.00034e -2.5t cos(22t) + 0.087e¯2.51 sin(22t) – 0.0072e 8t

Q: g. L[t sin²2t]] h. L[x4 cosh 3x]

A: to find the Laplace transform Rules:

Q: 8. t* – t² – t + sin v2t

A: according to our guidelines we can answer only three subparts, or first question and rest can be…

Q: - e2t)2 t cos3t

A:

Q: sinat dt 2.1. Use Laplace transforms theory to compute

A:

Q: Find and simplify the Laplace transform of the following functions, indicate the formula number from…

A: Formulas:Given the function .Consider .Differentiating, we getThis is essentially our function u(t).…

Q: 1- cos at Q6. Find the Laplace transform of following functions (a) t sin at (b) t

A:

Q: o. £[x2e-3* sinh 4x] L[x²e¯

A:

Q: TT f(t) = 10 cos(t 6,

A:

Q: 10. Find the Laplace transform of f Ct)= t sin 4t cos t• 58 C. 852 (s?+16)3 45 b. 4s2 do 3 (s?+I6)°

A:

Q: Find the Laplace transform of the following functions: b) t5/2 sinh 4t

A: Solution :-

Q: . Calculate the Laplace transform L {sin? t – cos²t}. -

A:

Q: Find the laplace transform of cos at using the formula L{f (t)} | e"f (t) dHencefind the laplace…

A:

Q: 2as L{t sin(at)} = %3D (s²+a²)²

A: We can derive it using the definition of Laplace transform or by using some identify or formula.

Q: Find the Laplace transform for each of the following fu (a) f(t) = (t – cos4t)° .(Hint: Use…

A:

Q: Find the Laplace transform of the following: 1. e3t cos 2t

A:

Q: . Find Fourier cosine transform of - and deduce that 2. bx e 1 e V2m log р ға cos px dx

A:

Q: 8. cos mt sin nt (m ‡n)

A: cosAsinB=12sinA+B-sinA-B and  ℒsinat=as2+a2, where a≠0 We have cosmt sinnt=12sinm+nt-sinm-nt

Q: 2 - ƒ (t) = sin 0.5t + ²⁄t – 3 8 cos 32t

A:

Q: Solve for the Laplace transform. 1.e sin2t

A:

Q: 1. Find the Laplace transform L{3t² +t5} a. b. L{2e*t sin 4t} L{t* + 2t3 – 4t² + t + 1} с.

A: We want to find the Laplace transforms.  Part(a) We have to find L{3t2+t5} Now, we have a formula:…

Q: Determine the Laplace Transform of cos(2/3t) cos (V31) Note:

A:

Q: . Determine the following values for the Laplace transform

A: Determine the following values for the Laplace transform

Q: Determine the Laplace Transform of the following functions. Show your detailed solutions. cos 3t 4.…

A:

Q: Find the laplace transform of cos at using the formula £{ƒ (t)} = est f (t) dt. Hencefind the…

A:

Q: Find the Laplace transform of the following: 1) sin t cos t

A: Laplace transform of f(t) is defined as  Lf(t)=∫0∞e-stf(t)dt. Also, Lsinat=as2+a2 ..........(1)…

Q: 4. (a – bt)?

A: Consider, a-bt2Suppose ft=a-bt2Then ft=a2+b2t2-2abt

Q: Determine the Laplace Transform of e 12 cos v 7t + sinV5 - 3

A:

Q: Determine the Laplace Transform of the following functions. Show your detailed solutions. 3.…

A:

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: Q2- Find the Fourier Transform for f (t) =A cos o,t, where o, = 2n fo %3D

A:

Q: d. L[3x7/2] L[6t10/3] e. f. £[x3 sinh 4x] -O

A:

Q: 2. t5/2 sinh 4t

A: The solution is given as