How does a capacitor work under AC?

I am confused about one of the core fundamentals of electrical components. How does a capacitor work under AC conditions? I know that a capacitor has two states (transient and steady.) This happens for DC circuits as well. Let us assume that we have built an AC RC circuit with a sinusoidal source. Initially the capacitor will be in its transient state as it was completely chargeless beforehand. We already know that a capacitor tries to hinder the change in its potential difference so when a source tries to induce charge, it obstructs and gets charged gradually and hence potential difference across it changes slowly depending on its capacitance. At the initial stage the capacitor shows some weird behavior but eventually it gets stable which we call the steady state of the capacitor. During steady state, the capacitor has its potential difference changed sinusoidally. If the capacitor intends to obstruct the change in its potential difference then why is it able to change that so easily in steady state? It is understandable for lower frequency, but at higher frequency shouldn't it pose some problems as it has to change its potential difference almost abruptly? Again if it can change so smoothly along a sinusoid then why is there a transient state to even start with? I mean in steady state there is also some point when \$V_C = 0\$ but still it is able to change its voltage so smoothly but at the initial stage it acts weirdly.

\$\begingroup\$ What is the weird behaviour you mention? Capacitors don't have states; they always follow the same simple rule with no weird behaviour. \$\endgroup\$

\$\begingroup\$ I mentioned about the steady state analysis and transient state analysis of capacitor \$\endgroup\$

\$\begingroup\$ @MSKB There are no two states. There will be a transient only if you apply a transient yourself. Please show which kind of circuit you are simulating to know where the transient comes from. If you don't want a transient then you need to set up the simulation conditions to start from a scenario as if the simulation had already been running forever or at least long enough that the transient caused by non-steady initial conditions have settled below the level you want. \$\endgroup\$

\$\begingroup\$ @Justme I know about the initial condition thing but I wanted to know how capacitor works at the initial phase \$\endgroup\$

\$\begingroup\$ @MSKB It does not work any differently at any phase, it's just a capacitor. Your circuit just does not start from a steady state. Same as applying a DC step to a capacitor, it takes time for the circuit to settle to new DC conditions. \$\endgroup\$