Assignment
Q.1 Find the Laplace transforms of the following functions:
(a) t^{2} + 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/s^{2} + 25, (iii) 1/s(s+1)
Q.3 Find the Laplace transform of the following functions.
(i) te^{at}, (ii) cos^{2}3t
Q.4 Show that α[t cosωt] = s^{2} -ω^{2}/(s^{2} + ω^{2})^{2}
(a) Find the Laplace transform of e^{at} sin ωt.
Find the Laplace transform of the following:
(i) e^{t}sin t, (ii) e^{-t}sin(ωt + θ) , (iii) 2t^{3}e^{-t/2}.
Q.5 Find f (t) for the following
F (s) = α[ f (t)].
(i) Π/(s + Π )^{2}, (ii) s - 2/(s^{2} - 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