Answer Happy

Consider the following RLC circuit with an input voltage denoted as x(t), and an output voltage denoted as y(t). R + L X(0) с y(t) Figure. An RLC circuit. (a) (3 points) Find the differential equation relating X(t) and y(t) if y(t) is considered the system output across the capacitor C. (b) (3 points) Let H(w) denote the system function (i.e., the frequency response of the system). Now, determine the magnitude and phase responses of H(w) using part (a) for the following periodic input voltage signal with period 21. x(t)= =en (1) (c) (4 points) Now determine the output y(t)of the system across the capacitor if the input is given by the following periodic input voltage signal with period 21. Assume that R=122, L=1H, and C=1F. x(t)=1+cost +cos 2t (2)