Question

Question asks for Laplace transform of

f(t)=t^2 u(t−1)
Hint given rewrite in terms of t-1 first

Answer 1

f(t) = t 2 [u(t − 1) − u(t − 2)] − 5[u(t − 2) − u(t − 3)] + (sin t)u(t − 3)

Note that this can be further simplified as:
f(t) = t 2u(t − 1) − (5 + t 2 )u(t − 2) + (sin t + 5)u(t − 3)

We would express f(t) as f(t) = f1(t)[u(t − t0) − u(t − t1)] + f2(t)[u(t − t1) − u(t − t2)] + +fn−1(t)[u(t − tn−2) − u(t − tn−1)] + fn(t)u(t − tn−1)

I hope this helps.