Question #43320

The question tests the student's ability to analyze forced oscillations in an AC circuit, specifically distinguishing between the natural frequency of an LC tank ($\omega_0 = 1000 \text{ rad/s}$) and the driven frequency ($\omega = 2000 \text{ rad/s}$).

A common trap is assuming the LC circuit resonates at its natural frequency regardless of the source, leading to the incorrect conclusion that the energy is constant ($0.00 \text{ J}$ work done).

Another trap is calculating the maximum energy of the capacitor ($0.16 \text{ J}$) but forgetting that the inductor holds a minimum non-zero energy ($0.04 \text{ J}$) at the exact moment the capacitor is empty, because the driven frequency forces an unequal reactance balance.

This requires applying phasor rotation to find the true steady-state voltage and using the work-energy theorem to equate the work done against conservative forces to the net change in the tank's electromagnetic energy.