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If the input current is of the form I_N sin(wt), of a parallel RLC circuit, determine the steady-state output voltage and the steady-state inductor current.

Engineering
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So far just for the source being "IN" for voltage I have \[\frac{ dv_{out}^2 }{ dt^2 } + \frac{1}{RC}\frac{dV_{out}}{dt} +\frac{V_{out}}{R} - \frac{1}{C}\frac{dI_N}{dt} = 0\]
When given \[I_Nsin(\omega t) = (I_C + I_L + I_R)\sin(\omega t)\] I get stuck because I am unsure if I am suppose to derive for \[[I_Nsin(\omega t)]\]
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Other answers:

for steady state conditions Z = R||sL||1/(sC) where s = j (2 PI/T) t =j w t V(t) out = I_N sin(w t) Z This works for steady state ie after all transients die out, its a result using Laplace Transforms.

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