How to find the convolution of e^t and sin(2t)

[errordude]

Homework Statement

Hi, can anyone help me to determine the convolution for the 2π periodic function f(t)=e^t and sin2t

 

[Mark44]

Someone can probably help you but I doubt they will until you show some effort at working this for yourself.

According to the rules of this forum (https://www.physicsforums.com/showthread.php?t=5374),

On helping with questions: Any and all assistance given to homework assignments or textbook style exercises should be given only after the questioner has shown some effort in solving the problem. If no attempt is made then the questioner should be asked to provide one before any assistance is given. Under no circumstances should complete solutions be provided to a questioner, whether or not an attempt has been made.​

 

[errordude]

well i know how to write e^t as a 2π periodic Fourier series but then what?

 

[Mark44]

What's the definition of the convolution of two functions? When you posted this problem, you deleted sections 2 and 3 about Relevant equations and your efforts at solving the problem.

 

[sutupidmath]

You don't need to use FOurier transforms for this problem. It is quite simple indeed, just go to the definition of the convolution of two functions, as was suggested here all along:

$$f\ast g=\int_0^tf(\alpha)g(t-\alpha)d\alpha$$

Now just substitute your functions instead of g and f. Hint: inside the integral i would let g(t-alfa)=e^(t-alfa), it makes the integration process easier. You know how to integrate, right?