Need an expression for v(t) in RC circuit

[cupoftea]

Hi,
I need to find an expression for V(AAA) at time t.
So i will have to use complex numbers i believe, would you say this is the best way?
Then i will go from frequency domain to time domain.
Ill use the mains as the reference phasor.
Ill start it later when i have time, but am just pre-planning now.

LTspice and jpeg attached

 

[FvM]

Don't understand what you try to achieve, input is sine, so output will be sine as well. Can calculate magnitude and phase without switching to time domain.

 

[D.A.(Tony)Stewart]