Question

Laplacetransform:
The solution of this wants a u(t-?) at the end of the inverse laplacetransform. I would highly appreciate it if someone could explain why, and if my answer is correct or not, regardless of not having u(t-?) at the end. *Screenshot of my task below*

Answer 1

My work: http://prntscr.com/3nzvxv

Answer 2

when you say
\((t-1)^2\)
if you do not mention anything else,
it is assumed that domain of t is from
\((-\infty , \infty )\)

so,
Laplace inverse of 2/s^3 e^-s is NOT (t-1)^2

it is (t-1)^2 with the condition that t>1
makes sense till here ?

Answer 3

i mean you understand why saying
Laplace inverse of 2/s^3 e^-s is (t-1)^2
is incorrect ?

Answer 4

So u(t-1) at the end is just a way to say that t > 1 ?

Answer 5

exactly!

see, if you know the definition of u(t) , you'll know that it = 1 from t>=0 and 0 from t<0.

and to represent (t-1)^2 , t>1 mathematically,
we multiply it by u(t-1)

so, from -infinity to 1, (t-1)^2 u(t-1) is 0 because u(t-1) is 0
and from 1 to infinity
(t-1)^2 u(t-1) is just (t-1)^2 because u(t-1) will be = 1

Answer 6

Thank you :)

Answer 7

welcome ^_^