Question

Sketch the following functions and find the Laplace transforms:

A) LaTeX: f(t)=u(t)+3u(t-1)-2u(t-2)-2u(t-3).
B) LaTeX: f(t)=2u(t+2)-3u(t+1)+4u(t-1)-3u(t-2).
C) LaTeX: f(t)=tu(t)-(t-2)u(t-2)-2u(t-4).
D) LaTeX: f(t)=tu(t)-(2t-4)u(t-2)+(t-4)u(t-4).

Answer 1

hello attached is the detailed solution

Explanation:

Laplace transform of the functions and the sketches are attached below

A) f(t) = u(t) + 3u(t-1) - 2u(t-2) - 2u(t-3)

F(s) =
`(1 + 3e^(-s) -2e^(-2s)-2e^(-3s) )/(s)`

B) f(t) = 2u(t+2) - 3u(t+1) +4u(t-1) - 3u(t-2)

F(s) =
`(2e^(2s) - 3e^s + 4e^(-s) -3e^(2s) )/(s)`

attached below is the remaining part of the answer