LC circuit

Still examinable, and worth saying so: LC circuits sit in the current AP Physics C: E&M course description, effective Fall 2024, as Topic 13.6. They are absent from AP Physics 1, AP Physics 2 and AP Physics C: Mechanics.

What is required is short. Three essential-knowledge statements and no boundary statement:

• 13.6.A.1 in a circuit containing only a charged capacitor and an inductor, the maximum current in the inductor can be found using conservation of energy within the circuit.
• 13.6.A.2 the time dependence of the charge stored in the capacitor can be modeled as simple harmonic motion, with the derived equation $\dfrac{d^2 q}{dt^2} = -\dfrac{1}{LC} q$.
• 13.6.A.3 the angular frequency follows from that differential equation: $\omega = \dfrac{1}{\sqrt{LC}}$.

Only the second of those is on the equation sheet. The differential equation is not printed; the angular frequency is, written there as $\omega_{LC}$.

The simple-harmonic correspondence is exact rather than loose. Charge plays the part of position, current the part of velocity, inductance the part of mass, and the reciprocal of capacitance the part of the spring constant. Energy sloshes between the capacitor's electric field and the inductor's magnetic field, and 13.6.A.1 asks you to equate $\tfrac{1}{2}Q^2/C$ at maximum charge with $\tfrac{1}{2}LI^2$ at maximum current.

The words RLC, damping and resonance appear nowhere in this course description. An undamped LC loop is the whole of it.