How to Simplify Laplace Transform with 3 Terms

[winbacker]

"easy" Laplace Transform...help!

Homework Statement

Evaluate L{(e^-2t)*t*sinht}

Homework Equations

translation theorem

The Attempt at a Solution

Just to clarify: the contents of the bracket is the product of 3 terms:
e^-2t (e to the power of -2t)
t
sinht

all multiplied together.

I am ok with finding the laplace of 2 term products but with 3 terms I do not know where to begin. All I can think of is that the presence of the euler term suggests the use of the 2nd translation theorem.

Any help would be appreciated.

 

[rock.freak667]

Start with L{sinhkt}, I hope you know what this is.

Now use the fact that L(tf(t)}= -F'(s)

Now just apply the shift property for L{e^-2tf(t)}

 

[phsopher]

You can express sinh t in terms of e^t and e^-t. Do that and combine all the exponentials together. That way you can express the whole thing as a sum of Laplace transforms of t at different points.