# Find the laplace transformation.

• Dec 12th 2011, 02:29 AM
Find the laplace transformation.
Find the Laplace transformation of the piecewise function.

f(t) = t+1, 0≤t≤1
f(t) = t^2, t>1

Sketch the graph of f(t)

i use the g(t)[u(t-a)-u(t-b)] and i get:

(t+1)[u(t-0)-u(t-1)]+(t^2)u(t-1)
and that gives:
(t+1)-(t+1)u(t-1)+(t^2)u(t-1)
and then i can take the Laplace
L[t]+L[1]+L[(t+1)u(t-1)]+L[(t^2)u(t-1)]

after much calculation i got answer which was wrong
I'm pretty sure i messed up trying to take the laplace of "L[(t+1)u(t-1)]+L[(t^2)u(t-1)]"

Any help?
• Dec 12th 2011, 04:21 AM
mr fantastic
Re: Find the laplace transformation.
Quote:

Find the Laplace transformation of the piecewise function.

f(t) = t+1, 0≤t≤1
f(t) = t^2, t>1

[snip]

Why not substitute f(t) into the definition of the Laplace transform and calculate the answer from 'first principles' ....
• Dec 12th 2011, 10:19 AM
Re: Find the laplace transformation.
You have intrigued me... What are "first principles"? I haven't heard my teacher use that term with laplace transformations.
• Dec 12th 2011, 11:30 AM
mr fantastic
Re: Find the laplace transformation.
Quote: