What is the amplitude of current in LC oscillations Since there is no resistance in an LC circuit (not attached to an AC source), what's stopping the current from rising to infinite. And if resistance is provided by the inductor by self induction, then why does the current become infinite when an AC source is added to an LC circuit at resonant frequency? what am i missing?
 A: 
what's stopping the current from rising to infinite

Assuming no driving voltage, typically the capacitor starts with some finite amount of charge, or a finite amount of current is in the circuit. This is analogous to a mass-spring system that starts at a finite displacement or a finite initial velocity.

And if resistance is provided by the inductor by self induction

An ideal inductor does not provide resistance. It provides reactance, which is a "resistance" to a change in current. The main difference to point out here is that resistance dissipates energy while reactance does not. This is analogous to the mass-spring system where inertia "resists" a change in velocity.

then why does the current become infinite when an AC source is added to an LC circuit at resonant frequency?

Because the AC power source is providing more and more energy without any of it being dissipated.
A: The wiki entry is a tolerable intro to LC circuits.
https://en.wikipedia.org/wiki/LC_circuit
You will also want to read about Lenz's law here.
https://en.wikipedia.org/wiki/Lenz%27s_law
In an LC circuit, the inductor attempts to decrease changes in current according to Lenz's law. So as the current rises the inductor tries to slow the rise. As the current falls the inductor tries to keep it going. In each case this works through changes in the magnetic field happening in a way that tends to oppose the changes in the electric current.
This provides a limitation on the current. The faster the current is rising the more the inductor resists the rise.
