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Laplace Transforms

  1. Dec 7, 2008 #1
    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. jcsd
  3. Dec 7, 2008 #2


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


    Where L{f(t)}=F(s)
  4. Dec 7, 2008 #3
    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....
  5. Dec 7, 2008 #4


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    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.
  6. Dec 7, 2008 #5
    correct! i saw that after i posted that, hehe
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