Damped Oscillations Start with a Delay
Since you didn't post a circuit diagram, most of what follows is speculation, but your waveform is very similar to what you see in any switching regulator that's operating in discontinuous mode.

When you turn on your MOSFET, you are "charging" the coil with a certain amount of current. At the moment when you turn off the MOSFET, this current still needs to flow. Since the current can't flow through the (smallish) capacitor, it is forced to flow through the "body" diode of the MOSFET (or some other diode you have in the circuit?), at least until it drops to a value that allows the voltage of that node to rise above zero volts. At that point, the diode stops conducting. Now the MOSFET is truly "open circuit" and you see the oscillations you expect.

OK, now that you've posted a diagram, I can see what's going on. When the gate signal goes high, this enables current to flow through the MOSFET, because the source is essentially tied to ground through the diode and the coil. Current builds up in the coil as described above, because it has a positive bias across it. When the gate signal goes low, the inductance of the coil pulls the source terminal low enough (a negative voltage) so that the MOSFET is still on, but now the magnitude of the current is decreasing instead of increasing, because the coil now has a negative bias across it. Once the current decays sufficiently to allow the MOSFET to cut off, the remaining residual current drives the oscillation you see in the latter part of each cycle.