# Laplace Transforms

1. Dec 7, 2008

### Nubcakes

Recently I've been working with Laplace Transforms and for the most part I am finding the simple ones to be very easy. However when they start looking like this:

... I start to falter, or atleast I think I am.

Since there are effectively 2 parts I see in this equation, I'd assume you'd just transform each part and multiply them together like so:

... However, the stated answer is as follows;

Can anyone point out how you do these problems? Rather Laplace Transforms where you have 2 parts{Such as (T^4)*(sinH(9T)) }?

Thank you for your time and sorry for my god awful handwriting!

2. Dec 7, 2008

### rock.freak667

You'd need to use the Shift property which states that

L{eatf(t)}=F(s-a)

Where L{f(t)}=F(s)

3. Dec 7, 2008

### jmarcian

use this...

=

just one of the laplace transforms from the table, usually given...

as for the two part equation you have (t^4)(sinh(9t)), i havent really seen a hyperbolic function in a Laplace transform, but i would start by possibly transforming sinh(9t) into exponentials....

4. Dec 7, 2008

### rock.freak667

For the hyperbolic sine, the OP can also find L{sinh(kt)} from the table, then use the general transform for L{tnf(t)}=F(n)(s). Where F(n) means the nth differential.

5. Dec 7, 2008

### jmarcian

correct! i saw that after i posted that, hehe