# Thread: Help with Laplace Transforms!

1. ## Help with Laplace Transforms!

I hope am in the right topic section hear i have this question i need guidance with its a laplace transform still kind fuzy on this topic the question is

find the laplace trasnform of $\displaystyle u(t-2)(t^2+4t-5)$ i dont know what to do going over my notes and txt i think its a second shifting theorm question so L{u(t-a)f(t-a)}=e^-asF(s) but stilll am not sure about it being first or second or what the difference itself is, any help please and if anyoe can guide me to some more examples i need help with thiese thanks!

2. Originally Posted by zangestu888
find the laplace trasnform of $\displaystyle u(t-2)(t^2+4t-5)$ i dont know what to do going over my notes and txt i think its a second shifting theorm question so L{u(t-a)f(t-a)}=e^-asF(s) but stilll am not sure about it being first or second or what the difference itself is, any help please and if anyoe can guide me to some more examples i need help with thiese thanks!
I think you need to be more clear... you have u's and t's in your function, and I'm not sure what is what. Is u(t) the unit step function, which is 0 for $\displaystyle t<0$ and 1 for $\displaystyle t\geq 0$?

3. al am asked in my question is find the laplace transform of
u(t-2)(t^2+4t-5) ? lol am sure its one of the shifting theorms but not sure how to apply it

4. I'm assuming that it's already in the correct form, namely $\displaystyle u(t-2)f(t-2)$.

So if $\displaystyle f(t-2) = t^{2}+4t-5$, then $\displaystyle f(t)= (t+2)^{2}+4(t+2)-5 = t^{2}+8t +7$

and $\displaystyle F(s) = \mathcal{L} [t^{2}+8t+7] = \frac {2}{s^{3}} + \frac{8}{s^{2}} + \frac{7}{s}$

$\displaystyle \mathcal{L} [u(t-2)f(t-2)] = e^{-2s}\Big( \frac {2}{s^{3}} + \frac{8}{s^{2}} + \frac{7}{s}\Big)$

5. where did the f(t-2) come from? is it becuase i have to have both u and f the same shift and it became t+2 becuase of the shift correct?

6. Originally Posted by zangestu888
where did the f(t-2) come from? is it becuase i have to have both u and f the same shift and it became t+2 becuase of the shift correct?
I'm assuming that what's given is u(t-2)f(t-2). But the theorem calls for the transform of f(t).