The oscillation decay time is OVERDAMPED so there is none if you had R=10, L=100uH, C= 100uF so the voltage rise time or current decay time T=RC here 10*100uf= 1ms with voltage at 64% of target or steady state.
I added realistic ESR of the cap , choke and voltage source which must always be considered in any analog design when considering Q values for Q=1/ζ with damping factor ζ.
Graphical Solution using RLC Nomograph expects Zo=1 Ohm and with series R=10 to have Q=0.1overdamped and RC= 1ms pulse decay time.
Now if you short the 10 Ohms what decay you get of the oscillation envelope is your ESR total in the loop. ( we call it DCR for chokes)
Read the graph see the resonant frequency from the intersection of 3 variables to get the 4th (resonant frequency) You can choose any 3 of 4 variables or just 3 as in RC,f-3dB.
Or add your expected ESR's and simulate
But be aware that short circuiting the electrolytic or e-cap can result in oscillations that momentarily reverse the voltage more than it's 10% tolerance perhaps to short of time to cause permanent damage if done only a few times.
e.g. with ESR values reduced.