Period of function

**horan6** · December 16th 2010, 04:54 PM

Considering the function $u(t,x)=\sum_{h=1}^{\infty}\left(a_{n}\cos\frac{n\p i}{L}ct+b_{n}\sin\frac{n\pi}{L}ct\right)\sin\frac{ n\pi}{L}x$

I know that the period of this function is $2\pi/L$ , but I am not sure how to prove it. I tried plugging in the period for t and reducing, but didn't get very far. Is this the right approach? Can anyone help with this?

Thanks in advance!

**snowtea** · December 16th 2010, 05:51 PM

If your period is $T$ , then $u(t+T,x) = u(t,x)$ for all $t$ and $x$ .

**SammyS** · December 18th 2010, 08:43 AM

Originally Posted by snowtea

If your period is $T$ , then $u(t+T,x) = u(t,x)$ for all $t$ and $x$ .

Actually, if $\displaystyle T$ is the period, then $\displaystyle u(t+kT,x) = u(t,x),$ for any integer, $\displaystyle k$ .

So, you need to show that $\displaystyle T$ is the smallest value for which $\displaystyle u(t+T,x) = u(t,x)$ is true.

Thread: Period of function

LinkBack

Thread Tools

Display

Period of function

Similar Math Help Forum Discussions

[SOLVED] Future value annuities with a different payment period to the compounding period.

Help with function and its period

Which period is this function?

period of function

Period Function:Graph

Search Tags