Consider a simple circuit like this:



The tank on the right is an oscillator
and the amplifier provides in-phase "boost" to the tank to keep the oscillations going.
its controlled by the feedback from the lower capacitor.

1. When Vout starts rising above the baseline ( 0 - 90 degree of sinusoid ) the center capacitor is receiving current from the inductor and increasing its voltage.
Flow of current is like C <== L
now the amplifier provides in-phase push which makes Vout even higher and stronger.

2. so the amplifier action charges the center capacitor more and more. So flow is like Amplifier ==> C makes C have more voltage

But, what is the effect of the amplifier action on the inductor ?
The amplifier also sees the inductor and should push against its current ?

Graph
Red - Vout = Vc
Green - Amplifier Action
Blue = L Current

 

To me it is not quite clear what you are asking - however, perhaps the following helps:

In your circuit, I cannot see any resistive part (and losses within the inductor as well as capacitor can never be avoided). Hence. you have no IDEAL tank circuit - and it is the purpose of the amplifier to compensate all the losses (which are not shown in your circuit).
Technically spoken: We need a loop gain of unity at a certain frequency - and this makes an amplifier necessary. Due to unavoidable losses a passive circuit can never have unity loop gain without an amplifier.

 

The L-C pair is not an oscillator, it is a series tuned circuit. Only with amplification is there an oscillator. And the feedback connection is incorrect as well. There are MANY tests that discuss oscillators to eny extent you desire, and they have already done so, therefore I suggest reading them. Or at least one of them.

 

The feedback connection might be right if an inverting amplifier is used (like a single transistor stage).
The circuit needs completing with a proper load resistor and power connections, and some form of an actual amplifier to get oscillations.
silvermoon where did your graph come from? Is it based on just the LC circuit ( no resistance is "ideal", really, as it will not decay and doesn't need an amplifier) You need resistances to represent a real circuit as LvW mentioned then you can see what an amplifier will do to assist.

 

Certainly before any useful analysis is possible a real world circuit is required. Withe the series LC arrangement shown a Colpitts oscillator is reasonable. So with a reasonable circuit you can do a reasonable analysis.