# Thread: solve by method of convolutions....

1. ## solve by method of convolutions....

ok so here is the problem, which by the way i thought was very straight forward...

$\mathcal{L}\left \{ \int_{0}^{t}e^{-\tau }cos \tau d\tau \right \}$

ok so i thought that i would just multiply the transforms by each other, but thats not what my book is showing.

for f(t)= e^-t and g(t)= cos t

so i tried multiplying (1/s+1)*(s/s^2+1)?

so where did i go wrong?

2. for this problem please ignore the f(t) and g(t)..this was my attempt at the problem. the question is asking me to solve the problem by method of convolutions, which I am unsure of how to do. i hope i didnt confuse ne one with this posting..

3. Originally Posted by slapmaxwell1
ok so here is the problem, which by the way i thought was very straight forward...

$\mathcal{L}\left\{\int_{0}^{t}e^{-\tau}\cos\tau\,d\tau\right\}$

ok so i thought that i would just multiply the transforms by each other, but thats not what my book is showing.

for f(t)= e^-t and g(t)= cos t

so i tried multiplying (1/s+1)*(s/s^2+1)?

so where did i go wrong?
Note that

$\int_0^t e^{-\tau}\cos\tau\,d\tau = e^{-t}\int_0^t e^{t-\tau}\cos\tau\,d\tau=f(t)\ast g(t)$

where f(t) = .... and g(t) = ....

4. <--- ok kool, i was wondering where the 1/s was coming from.

5. Originally Posted by mr fantastic
I know the latex is not working. I don't know what the problem is. But I'm sure you can figure out what I posted.
It turns out that it didn't like the f(t)*g(t) part. So I replaced it with f(t)\ast g(t) and it turned out alright. This may be the case because this is supposed to be a link of some kind, and having * in a link is a bit bizarre.