Measuring pulse length with ICP
Are you aware that the L and C tuned circuit are highly likely to to produce a series of oscillations decaying to zero and that your code must decipher the series of pulses coming from the comparator into something meaningful? 

Maybe you are also aware that the L and C energy produces a decaying sinewave centred around 0V and this could damage damage your comparator - the LM393 has an absolute input voltage of -0.3 volts and if exceeded could cause the device permanent damage. At the very least it will screw up the signal you hope to measure.

If you wish to keep the signal as intact as you can (such as in a metal detection application) you'd be wise to put a series resistor between comparator input and tuned circuit then bias this at about half Vcc with half Vcc on the other comparator input.