I have a function $v : \mathbb{R} \rightarrow \mathbb{R}$ which describes the norm of the velocity of an object moving under gravitational forces. As the object describes a closed period path, hence the function $v$ is periodic, of period 1 let's say, and always positive, as it is the norm of the velocity.
I was thinking and couldn't find an answer, what is, if there exists, a pattern of the Fourier series coefficients.
If someone knows the answer that would be great and an explanation would be even more appreciated. Thank you!
Marius
Best Answer
I am sorry for being hasty in posting and then actually answering my own question. If the Fourier Series is under the form $$v(t) = \sum\limits_{k=0}^\infty[a_k\cos(2\pi k)+b_k\sin(2\pi k)]$$ then what is needed is just that for $a_0$ to be greater than the sum of modules of the other Fourier coefficients. This ensures that the sum is always positive.
Sorry for posting so quickly a question.
Although, I would be happy to hear other answers! :)