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