Find the Laplace transform Fs of the following ft 2 if 0 le

Find the Laplace transform F(s) of the following f(t) = {2 if 0 lessthanorequalto t

Solution

(a) Here L^-1{1-2s/((s-3)^2+5)

now break the function into two parts

= 1/((s-3)^2+1) - 2 s/((s-3)^2+1)

= e^3t sint - 2. e^3t.cost

(b) L^-1{ 18e^-3s/(S-2)(S+7)}

= 18 e^-3s. 1/(s-2). 1/s+7

= 18 u(t-3)(t-3)e^(t-3)