The lower NPN turns on to a certain extent, which turns on the upper NPN to a certain extent.
If either bjt remains off, then output voltage would be +10V. Instead your input signals set the 3 transistors fluctuating.
Calculate the resonant frequency of the RLC tank at top. By itself it does not oscillate or resonate. However you're watching to see if harmonic oscillations develop in other sections of the circuit. This could cause resonant action in the RLC tank, and that will cause fluctuations of your output voltage.