Consider a causal LTI system implemented as the RLC circuit shown in Figure P3.20. In th...

Consider a causal LTI system implemented as the RLC circuit shown in Figure P3.20. In this circuit, x(t) is the input voltage. The voltage y(t) across the capacitor is considered the system output.

(a) Find the differential equation relating x(t) and y(t).

(b) Determine the frequency response of this system by considering the output of the system to inputs of the form

(c) Determine the output y(t) if x(t) = sin(t).