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Laplace Transform (Linear Algebra)

  1. Apr 23, 2013 #1
    1. The problem statement, all variables and given/known data
    Evaluate the laplace transform of {t2e7tsinh(3t)}


    2. Relevant equations
    Laplace transform of {tnf(t)}=(-1)ndn/ds2 * F(s)


    3. The attempt at a solution
    I've replaced it with (-1)2d2L{e7tsinh(3t)}

    I'm not sure how to proceed, though, as I don't really see how to take the laplace without somehow splitting up these functions. Do I use a unit step function? How would I use it if so? I'm not really sure what to do here

    Thanks for any help.
     
  2. jcsd
  3. Apr 23, 2013 #2
    The Laplace transform of a function that has been multiplied by an exponential function can be found using the shift theorem for the s-axis. Do you know this theorem?

    BiP
     
  4. Apr 23, 2013 #3
    Is this the theorem you were referring to?

    L{e-asF(s)}=f(t-a)*UnitStep(t-a)
     
  5. Apr 23, 2013 #4

    Ray Vickson

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    Science Advisor
    Homework Helper

    You can write ##\sinh(3t) = \frac{1}{2} \left( e^{3t} - e^{-3t}\right),## and proceed accordingly.
     
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