1) Compute the Laplace transform function F(s) of the function f(t) using the definition: F(s) = [() = ef(t)dt. (Refer on Table 1 for the answers) -st a) cosh kt and sinh kt b) eat sin kt und et cos kt c) t" and t"eut

Q: 2S-1 s²-6s+187 L-¹ {

A:

Q: 3 Laplace Transform of (sin(2s))³

A: Given:

Q: be separated into additive components before undergoing Laplace Transformation. The Laplace…

A:

Q: Check that the Fourier transform of: is g(t) f(w) = { 0 = sin at t -a<w<a rest

A:

Q: If x=t-4, find L[(xe¯x)]

A:

Q: Find L-1 (3) 5s-6 s2 –3s

A: We have to find inverse LAPLACE TRANSFORM of given function.

Q: 2t-3

A:

Q: y" + y = 10 cos t e-t + 2 t?

A: Consider the given differential equation:

Q: ėt, Cost Cos 2t

A:

Q: transform Find the Laplace [(+-1)u(t-1)-[(+-1) (+-2) U

A:

Q: Fis)-S-65-15 -359

A: Solution is given below:

Q: determine the laplace transform

A: Given,          f(t)=3sin(bt)cosh(bt)

Q: Fourier transform Laplace transform O True O False

A: We have to state true or false The Fourier Transform is particular Laplace transform.

Q: Find L. T. for each of the following functions: (t-4)²u(t-4), (t-3)e-2(t-3) sin 4(t-3)u(t-3).

A:

Q: L[sin(3t - 4n)]

A:

Q: _-_-7/57 = 1778 ++ (5)) pust

A:

Q: f *g =g *f , where (*) is the convolution in Fourier transform. Select one: True False

A: Given: (*) is the convolution in fourier transform. To prove:  f*g=g*f. Proof: It is known that…

Q: Using Laplace transform to Sálce differen tral equation of the form fCS) - 82+3st1

A: By the method of partial fraction we can solved the problem

Q: Laplace transformation f(t) = e ^ 2t cos2t

A: Laplace transformation f(t) = e ^ 2t cos2t

Q: 1- cos t Find the Laplace transform of

A:

Q: erform the Laplace Transform Show your Solution 2e-5t sin 10t + 6e-5t cos 10t

A:

Q: a. (t-e-4t)² sec²4t -tan 4t]

A:

Q: Deduce the Fourier transform of -It g(t) = (1+|t|)e-l

A: Given that,  The function is- gt=1+te-t Since, The Fourier transform is defined as Gw=∫-∞∞gte-iwtdt…

Q: F(@) = ? -1 f(t) 1

A:

Q: Determine the Fourier transform of the function f(t) = e-cltl.

A:

Q: y = 3sinh (3t) 3 s² +9 A) 6 s² +9 3 S² - 9 6 S²-9

A: Given function is y= 3sinh(3t)

Q: HCt-2) Cosh(6(t-2))est ?

A: Given: Ht-2cosh 6t-2e8t

Q: 2. f(t) = (t + 2)² et %3D

A: We need to find Laplace Transform of , f(t) = t + 22et We know Laplace Transform is given by , Lf(t)…

Q: estion * he Laplace transform of f (t) = t2 U(t - 3) is: F(s) = e -35 F(s) = e +.

A: Laplace Transform

Q: - FCS) いは %3D then-L (t" fra) fess %3D

A:

Q: 10s¯ + 8s + 29 inverse laplace ( (2s 3s + 7)- -

A: We have to find the partial fraction first.

Q: TT ㅠ (S+T) 2 6) L-¹ {

A: L-1πs+π2 To Do:We have to evaluate the inverse Laplace transform.

Q: -T: TR TR be ormation depined ) =(x+Qy= メ+2y-Zッコメ ec) Rang(T) the

A: Given Linear Transformation:  Tx,y,z=z+2y-z,2x+3y+z,4x+7y-z For kernel we solve homogenous system of…

Q: 1 (5+3)(s+7) Laplace Inverse Transform of.

A: