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- #1

So it says the average $\langle x\rangle$ is zero and the $x_{\text{RMS}} = \sqrt{\langle x^2\rangle}$ where

$$

\langle x^2\rangle = \frac{1}{\tau}\int_{-\tau/2}^{\tau/2}x^2dt

$$

The Fourier expansion of $x(t)$ is

$$

x(t) = \sum_{n = 0}^{\infty}A_n\cos(n\omega t - \delta_n).

$$

Then we obtain an integral of a double sum which simplifies down to

$$

\langle x^2\rangle = A_0^2 + \frac{1}{2}\sum_{n = 1}^{\infty}A_n^2.

$$

Then there is a note that $A_0 = \langle x\rangle$ which is supposed to be zero. How do I find the nonzero $A_0$ value?