Halliday, Resnick & Walker — Electromagnetic Oscillations and Alternating Current: Problem 40

40 A series circuit containing inductance \(L_1\) and capacitance \(C_1\) oscillates at angular frequency \(\omega\). A second series circuit, containing inductance \(L_2\) and capacitance \(C_2\), oscillates at the same angular frequency. In terms of \(\omega\), what is the angular frequency of oscillation of a series circuit containing all four of these elements? Neglect resistance. (Hint: Use the formulas for equivalent capacitance and equivalent inductance; see Module 25-3 and Problem 11 in Chapter 30.)