Assignment

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

(a) t² + at + b and (b) sin(2nΠt/T)

Q.2 Find f (t) 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

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

Find the Laplace transform of the following:

(i) e^tsin t, (ii) e^-tsin(ωt + θ) , (iii) 2t³e^-t/2.

Q.5 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

Find the Laplace transform of cosh at cos at

Q.6 Using Matlab and Laplace transform, find the solution of the following differential equation:

5y' + 2 y = sin t