Heat dissipated in an RLC circuit

[nautola]

Homework Statement

A 4 Ω resistor, 14 mH inductor, and 99 µF
capacitor are connected in series to a 65 V
(rms) source having variable frequency.
Find the heat dissipated in the circuit during one period if the operating frequency is
twice the resonance frequency.
Answer in units of J

Homework Equations

Vrms * R * ω^2/(Rω^2 + L^2(ω^2 -ω(0)^2)^2) = avg power

The Attempt at a Solution

I integrated the average power from 0 to ∏√(LC) because that was the time for one period. Then I got 8447.31 J. This is a massive number, which I'm sure is wrong. But I don't really know what I'm doing wrong.

 

[gneill]

Your Relevant Equation yields the real component of the complex current (RMS complex current, since you're starting with Vrms). Multiply it by R to find the average power (or, perhaps you meant to have R² in the numerator to begin with...)

A full cycle is $2\pi$ radians, so that T = $2\pi/\omega$.