Question

Express f (t) in terms of the Heavisides unit step function and find its Laplace transform:

f(t) = {(t2, 0 < t < 2) (4t, 2 < t < 4) (8, t > 4)

Answer 1

We get

f (t) = t2 + (4t – t2) u(t – 2) + (8 – 4t) u(t – 4)

f(t) = t2 + [4 – (t – 2)2] u(t – 2) + [– 4(t – 4) – 8] u(t – 4)

Taking Laplace transform on both sides, we get,