Funny,
I replicated the VIC in multisim and got the same waveform as your oscopse shows with the secondary and choke coils having the same inductance. I also got a much higher voltage than the transofrmer turns ratio could give, and I got a step charging voltage across the capacitor. I understand the AC part of the waveform, but what I don't understand is the AM part, why the oscillations build up, peak, and then die down.
I'm thinking the build up is the charging of the inductor to it's peak, the dying down is the energy being dissipated?