What happens when injecting a current at different instants in an oscillator?

[iVenky]

Hi,

I am reading the Hajimiri-Lee phase noise model, and got a question on that. If you have an LC tank circuit that is free-running and I inject a current i(t) (dirac current) at instants either t1 or t2 (shown in the figure), depending on when you inject the phase of the output changes (as shown). If I inject it at t1, then phase of the output changes while if I inject it at t2 only the amplitude changes but not the phase. What I don't understand here is when I inject the current i(t) at instant t1, shouldn't the amplitude also change just by superposition of oscillation waveform and the input i(t) energy? This is the part that's confusing to me. And what happens if I inject a really large i(t) that the resultant voltage exceeds the initial peak voltage to begin with, would the amplitude still change?

In the dV/dt and V plot, t1 corresponds to 'b' and t2 corresponds to 'a'.

Attached the image.

 

[NascentOxygen]

I'd say injection of current at t1 should change amplitude as well as phase.