You basically have 2 time constants at work here, assuming the capacitor is charged and the inductor is open circuit with no emf present when the 'switch' is closed to form a discharge path from the capacitor through the R and L....
The L & C will form a time constant at a particular frequency with a period of:
τ = 2∏ f √(L x C)
The second time constant is formed from the C and R and is exponential.
The resulting waveform will be an exponentially decaying sine wave with a period of roughly τ...
Hope this helps, I've skipped a lot of calculations as sometimes a guesstimate is adequate.
John.
__________________
A little knowledge is a dangerous thing - Googling is far worse!
"Almost" Good Answers: