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An AC voltmeter of large impedance is connected in turn across the inductor, the capacitor, and the resistor in a series RLC circuit driven by an alternating emf of 125 V (rms). The meter gives the same reading in each case. The angular frequency of the AC source is 4*sqrt(3) rad/s. The circuit is then disconnected from the source; the capacitor is charged separately and reconnected in series with the inductor and resistor. The resulting oscillations are underdamped. Find the angular frequency of the damped oscillations in rad/s.

1. 2 rad/s
2. 6 rad/s
3. 4 rad/s
4. 8 rad/s

Correct answer: 6 rad/s

Solution

At resonance V_L = V_C = V_R implies R = omega₀ * L = 1/(omega₀ * C). Using omega₀ = 4*sqrt(3) rad/s gives R/L = 4*sqrt(3), and 1/LC = 48. The damped oscillation frequency is sqrt(48 - 48/4) = sqrt(36) = 6 rad/s.

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