Question

Question # 1 a) State the definition of the Laplace transform of a function f(x) b) Hence determine the following transforms using the definition of Laplace transform ili. f(t) 3 ii. f(t) -sin 2t Determine the solutions of the following initial value problems using Laplace transforms c)

Answer 1

"Laplace transform is a frequency domain approach for continuous time signals irrespective of whether the system is stable (or) unstable. Laplace transform of function f(t) is defined by L[f(t)] = F(s) = integral^infinity_0 f(t) e^-st dt f(t) = e^3t L[f(t)] = integral^infinity_0 e^3t e^-st dt = integral^infinity_0 e^-1(s - 3) t dt = e^-(s - 3) t/-(s - 3)