Thread: Manipulating Laplace into form I need...

Hi all,

I've got something I need to take the laplace of, and it's in the form of

t^2 H(t-1)

I know to take advantage of the second shift theorem, I need to rearrange the left hand side so it has (t-1) in the t terms.

I also know that the final answer is
(t-1)^2 + 2(t-1) + 1, but I'm unsure of the method to consistently work through and get this solution.

From memory, it has to do with subbing in (t-1) into the t term, expanding out and doing balancing, but after mucking around for about 30 minutes I can't seem to get it out.

Can anyone please help with the process? Thank you.

P.s. Sorry for the non-latex math, I tried with it and am getting some weird errors.

Originally Posted by Peleus

Hi all,

I've got something I need to take the laplace of, and it's in the form of

t^2 H(t-1)

I know to take advantage of the second shift theorem, I need to rearrange the left hand side so it has (t-1) in the t terms.

I also know that the final answer is
(t-1)^2 + 2(t-1) + 1, but I'm unsure of the method to consistently work through and get this solution.

From memory, it has to do with subbing in (t-1) into the t term, expanding out and doing balancing, but after mucking around for about 30 minutes I can't seem to get it out.

Can anyone please help with the process? Thank you.

P.s. Sorry for the non-latex math, I tried with it and am getting some weird errors.

Note that t^2 = (t - 1)^2 + 2t - 1 = (t - 1)^2 + 2(t - 1) + 2 - 1 = (t - 1)^2 + 2(t - 1) + 1.

This sort of algebraic re-arrangment is what you have to do (and if you're studying at the level of learning about Laplace transforms then you're meant to be able to this sort of re-arrangement in your sleep).

Firstly, thank's I got the process now.

Secondly, yes I agree that I should know how to do it, but if I don't I need to learn how to do it. It's completely my fault, but I find math rather difficult. I would give my left arm to have half the understanding of math that you do. But alas, I don't.

In the mean time however, all I can do is post up my question's that I'm having trouble with and actually try and learn what I'm meant to - and fixing the holes in my knowledge, rather than not trying at all.