Find the solution of the differential equation - find the

Question

LAPLACE QUESTIONS TO BE SOLVED USING MATLAB

Part 1

Q. 1 Find the Laplace transforms of the following functions:

(a) t² + at + b and (b) sin(2nΠt / T )

Q. 2 Find f(t) f for the following F(s) = α[f(t)].

(i) 5/s + 3, (ii) 1/s² + 25 , (iii) 1/s(s + 1)

Q. 3  Find the Laplace transform of the following functions.

(i) te^at, (ii) cos²3t

Q.4 Show that α[t cosωt] = s² - ω²/(s² + ω² )²

Part 2

Q.1(a) Find the Laplace transform of e^at sin ωt .

Q.2 Find the Laplace transform of the following:

(i) e^tsin t, (ii) e^-t sin(ωt + θ ) , (iii) 2t³ e^-t/2.

Q. 3 Find f (t) for the following F (s) = α[ f (t)].

(i) Π/(s+Π)², (ii) s-2/(s² -4s + 5) , (iii) s/(s + 3)² + 1

Q. 4 Find the Laplace transform of

cosh at cos at.

Q.5 Using Matlab and Laplace transform, find the solution of the following differential equation:

5 y' + 2y = sin t