What happens when I connect an LC circuit to only the positive terminal of a voltage source?
Call the schematic as shown the "base state". There is no voltage drop across L1 or C1, so the top od SW2 is at V1.  SW2 ensures there is no voltage across R1.
When the switches change... L1 C1 charge as a resonant circuit. This is made more complex, because L2 (and C2 in parallel with R1) are all in parallel with C1.
Depending on Q (ratio of Lto C) there may be some ringing, but eventually ALL of V1 should appear across R1. C1 and C2 should both charge to V1. 
When the switches change back ? C1 discharges via L1. There may be ringing again, but you won't see it because nothing is connected.
C2 discharges via L2 and R1, until the voltage across R1 eventually returns to zero - the original state.