Chapter 5, Problem 94RE

  Root mean square The root mean square (or RMS) is another measure of average value, often used with oscillating functions (for example, sine and cosine functions that describe the current, voltage, or power in an alternating circuit). The RMS of a function f on the interval [0. T] is

     ${\bar{f}}_{\text{RMS}}=\sqrt{\frac{1}{T}{\displaystyle {\int }_0^{T}f{\left(t\right)}^{2}dt}}$.

  Compute the RMS of $f\left(t\right)=A\sin \left(\omega t\right)$. where A and ω are positive constants and T is any integer multiple of the period of f. which is $2\pi /\omega$.