All Problems

Electric Oscillations

Problem 4.108

How much (in per cent) does the free oscillation frequency ω\omega of a circuit with quality factor Q=5.0Q=5.0 differ from the natural oscillation frequency ω0\omega_{0} of that circuit?

Reveal Answer
ω0−ωω0=1−11+1/(2Q)2≈18Q2=0.5%\frac{\omega_{0}-\omega}{\omega_{0}}=1-\frac{1}{\sqrt{1+1 /(2 Q)^{2}}} \approx \frac{1}{8 Q^{2}}=0.5 \%
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