# Thread: Convolution of Laplace Transformation?

1. ## Convolution of Laplace Transformation?

Hi.

I am stuck on this question and not quite sure how to start it off.

Use convolution to find the Laplace transforms of

a. $\displaystyle f(t) = \int_0^t sin(t - \tau) e^{3 \tau}d\tau$
and b. $\displaystyle f(t) = \int_0^t \sigma(\tau) (t - \tau) d\tau$

.

Maybe I don't understand the whole concept of convolution. Any help would be great.

Thanks!

2. Originally Posted by lpd
Hi.

I am stuck on this question and not quite sure how to start it off.

Use convolution to find the Laplace transforms of

a. $\displaystyle f(t) = \int_0^t sin(t - \tau) e^{3 \tau}d\tau$
and b. $\displaystyle f(t) = \int_0^t \sigma(\tau) (t - \tau) d\tau$

.

Maybe I don't understand the whole concept of convolution. Any help would be great.

Thanks!
You should know that $\displaystyle LT[g(t) * h(t)] = LT[g(t)] \cdot LT[h(t)]$.

a. By definition, $\displaystyle f(t) = e^{3t} * \sin t$.

b. is left for you to think about.