Does anyone know what the laplace transform of 3tcosh(8t) would be?

Question

Does anyone know what the laplace transform of 3tcosh(8t) would be?

Answer 1

Check out #7 on the LaPlace table:  I'm pretty sure your answer comes out to be:

3*( s /  (s^2 -64) )

The u(t) is the single t coefficient, and the 8 from the cosh(8t) is alpha.

Answer 2

Well cosh(8t) =  s/ (s^2 - 8^2) which = s/(s^2 - 64).  the 3 is a constant out front, but that t infront is important.  That means you take the (-) derivative of (s/(s^2 - 64)) which using the quotient rule gives:

  - (s^2-64 - (s(2s))                 s^2 + 64                (numorator)

----------------------------- =  ------------------------

        (s^2 - 64)^2               (s^2 - 64)^2           (denominator)

then all that times the constant 3.