We are presented with a familiar first-order circuit: a capacitor driven by a Thevenin source. Now we have a sinusoidal drive that starts at t=0. so the differential equation is
RCdv(t)dt+v(t)=vI(t)=Vicos(ωt)u(t)
and we are given the initial state v(0−)=0.
We know how to solve this problem in the abstract.
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