claudia is trying to design an rc circuit to produce a steady state am

Question

) Claudia is trying to design an RC circuit to produce a steady state amplitude of 0.5volts when supplied with a periodic driving force of E(t) = cos(2t) volts. She is allowed to choose the resistance and capacitance and hence, the time constant T = RC of the circuit. Find the general solution for the voltage across the capacitor in this RC circuit and identify the steady state part of your solution. Note that your solution should depend on T. Validate your solution from part (a) in Matlab for the case where T = 1 and the initial voltage vo = 0. Create a plot which shows how the amplitude of your steady state solution depends on T and identify the value of T which gives the desired value of 1/2.