2. The RC circuit is shown in Fig. 1. Figure 1: The RC Circuit where v;(t) is voltage input, i is current, R is resistance, q is charge, C is

capacitance, v,(t) is voltage output and t is time. Considering a voltage input of v:(t) = cos(wt), where w = wave frequency, the RC circuit system can be described with the following first order differential equation \cos (\omega t)=\frac{d v_{o}(t)}{d t} R C+v_{o}(t) where the resistance R and the capacitance C are constants and vo(t) is the output voltage. a) Use Laplace Transforms to solve for the output voltage, v.(t), given the initial conditionthat vo(t) = 1 at t = 0.%3D b) Show that the steady-state solution can be expressed v_{o}(t)=\frac{1}{1+(\omega R C)^{2}}[\cos (\omega t)+\omega R C \sin (\omega t)] c) Given the steady state solution, find an expression for v.(t) in the low frequency limit.