Depending on the switching frequency, the circuit can work in two distinct mode.
MODE 1
If the switching frequency is less than the resonance frequency of the capacitor+transformer_inductor, The output will be a sine wave. Solve the differential equation for a series LC circuit where the the capacitor has an initial voltage. The output is a sine wave. But it is highly unlikely that the circuit will be working in this mode.
MODE 2
If the switch is closed only for a short time, and opened again for a large time, the following will happen...
1. When the switch closes, the transformer draws an input current from the capacitor.
2. When the switch opens, the current in the transformer is interrupted suddenly and this causes a large voltage spike. The 1K resistance on the secondary prevents current inrush when the air breaks down due to high voltage.
3. During the off-time, the capacitor also charges through R1.