Thread: 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?

Originally Posted by Aquameatwad

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' ....

You have intrigued me... What are "first principles"? I haven't heard my teacher use that term with laplace transformations.

Originally Posted by Aquameatwad

You have intrigued me... What are "first principles"? I haven't heard my teacher use that term with laplace transformations.

Equation (1) here: Laplace Transform -- from Wolfram MathWorld

I'd be amazed if your class notes and textbook don't have it, together with examples.

This class should be taught in 2 semesters than just one. Our teacher does the best he can in this short amount of time. thanks for the insight , i will look into it