(Linear, constant coefficient differential equation circuit models) The systems of most interest to us in this course have input-output models in the form of linear, constant-coefficient differential equations. As you know from ECE 210, systems like that are represented by linear circuits. Consider the RLC circuit shown below. Assume that ? = 10 , ? = 1 H, and ? = 0.008 F. C i ( t ) (a) Write a differential equation relating x ( t ) ( the input signal) with y ( t ) (t he output signal). (5 points) (b) Let X ( s ) and Y ( s ) denote the Laplace transforms of x ( t ) and y ( t ) , re spectively. Find H ( s ) = Y ( s ) / X ( s ) . Assume zero initial conditions. ( H ( s ) is called the transfer function of the circuit) (5 points) (c) Assume that x ( t ) = 0 for 0 and that y ( 0) = 2 , and the current in the circuit at time t = 0 is i ( t ) = 0 . Find y ( t )