Use the second shifting theorem to find the Laplace transform

[Rubik]

Homework Statement

Use the second shifting theorem to find the Laplace transform of

f(t) = {t², t<4
{t, t$\geq$4

Homework Equations

L{f(t - a)u(t - a)} = e^-as F(s)

The Attempt at a Solution

Okay so I applied the unit step function to get the equation into the form
f(t) = t² - t²(u)(t - 4) + t(u)(t - 4)
= t²(1 -u(t - 4) + t(u)(t - 4))

However now I get lost as I know it needs to be in the form f(t - a)u(t - a) and I see that the second part of equation is but the first part is confusing me I think maybe I am suppose to complete the square though I just can't see how?

 

[MisterX]

You've missplaced a parenthesis. There should be no t^3 power in your expression for f(t).

Anyway, you don't need to complete the square; that would not be appropriate. Think about what g(t₁) needs to be so that g(t-a) = t².

 

[Rubik]

Sorry but I am still not sure what to do with the t² but with my second term, t²(u)(t - 4) is right to do this..

L{t²(u)(t - 4)
= t² 8t +16 - 8t - 16
= (t - 4)² + 8t - 16)(u)(t - 4)
= ((t - 4)² _ 8(t - 4) + 16)(u)(t - 4)
= (2/s³ + 8/s² and here I am not sure what 16 becomes?)e^-4s

 

[LCKurtz]

It is a no-no to post the same question into two different places in these forums. I have just answered a similar question in your other thread:

https://www.physicsforums.com/showthread.php?t=523836

 

[Rubik]

Sorry I posted this before than saw you reply in my other thread so replied with the example I was working with.. should I have linked you to this thread instead is that still okay?