# Period of function

• Dec 16th 2010, 05:54 PM
horan6
Period of function
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?

• Dec 16th 2010, 06:51 PM
snowtea
If your period is $T$, then $u(t+T,x) = u(t,x)$ for all $t$ and $x$.
• Dec 18th 2010, 09:43 AM
SammyS
Quote:

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.