The LC circuit described does not oscillate as expected due to several factors, including insufficient inductance and resistance in the circuit. The inductor's low number of turns and the use of a basic multimeter limit the ability to detect high-frequency oscillations, which may occur at frequencies around 122 MHz. The circuit's oscillation is further hindered by the lack of a proper switching mechanism; using a quartz oscillator and transistors could help sustain oscillations. The compass and multimeter may not effectively measure the transient currents generated, especially at high frequencies. To achieve observable oscillations, modifications to the circuit's components and configuration are necessary.