# Homework Help: Use the second shifting theorem to find the Laplace transform

1. Aug 23, 2011

### Rubik

1. The problem statement, all variables and given/known data

Use the second shifting theorem to find the Laplace transform of

f(t) = {t2, t<4
{t, t$\geq$4

2. Relevant equations

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

3. The attempt at a solution
Okay so I applied the unit step function to get the equation in to 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?

2. Aug 23, 2011

### 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.

3. Aug 24, 2011

### 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

4. Aug 24, 2011

### LCKurtz

5. Aug 24, 2011

### 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?