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Need an expression for v(t) in RC circuit

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cupoftea

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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
 

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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.
 
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