# Laplace Transform (Linear Algebra)

1. Apr 23, 2013

### yesiammanu

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. Apr 23, 2013

### Bipolarity

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

3. Apr 23, 2013

### yesiammanu

Is this the theorem you were referring to?

L{e-asF(s)}=f(t-a)*UnitStep(t-a)

4. Apr 23, 2013

### Ray Vickson

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