Eheh I see, I should spend 90% of the time with the simulator and 10% on the breadboard, thanks for taking the time to put my circuit in the simulator!
So why on the first circuit do I get such a dc offset? After the buffer I should be getting 2.5v, but it could well be that the resistor divider is giving me 2.501 and then that .001 gets amplified and ends up showing up as a huge dc offset... I tried lowering the gain of the amplifier with the pot and no matter what I think I was still getting that offset so it has to be something else.
As for the 2nd circuit, the one with the cap, I am not using R6(nor the vgnd), and it turns out I get a nice oscillation as in your sim... that is pretty scary because the circuit shouldn't work at all
Thanks IanB for keeping me curious

BTW I happen to have a coil and a varcap that I can tune to 77.5Khz and I am hoping to receive the signal of an atomic clock that transmits in that frequency, this is just an excuse to learn about LC and hopefully some radio stuff

Now I'm still at the LC part

edit1: I tested the circuit with the clipped sinewave in my ltspice and I get a proper sinewave, how comes your simulator and mine dont agree?
edit2: I noticed your AC source has 0.1 volts of DC offset, and that is what is causing the 1volt dc offset at the output, did you put it on purpose?
I'm feeling close to understand something great!