Laplace transform of convolution with derivative in it

[tjosan]

Homework Statement

Hi,

I am wondering how to Laplace transform this expression

f(t)=\int^{\tau}_{0} g(\tau)f'(t-\tau)d\tau
or more precisely
f(t)=\int^{\tau}_{0} sin(8\tau)f'(t-\tau)d\tau

The f'(t-\tau) gets me confused.

Homework Equations

\int^{\tau}_{0} f(t-\tau)g(\tau)d\tau
and the laplace transform of that is:
F(s)G(s)

The Attempt at a Solution

I have no idea how to proceed.

Maybe
F(s)=8/(s^2+8^2)(sF(s)-f(0))

 

[damoj]

had the same question earlier this week

check out

https://www.physicsforums.com/showthread.php?t=537347