Question: The transfer function of an RLC circuit is H(s) = Y(s)/X(s) = 2s/(s 2 +2s+1). (a) Obtain the ordinary differential equation with input x(t) and

The transfer function of an RLC circuit is H(s) = Y(s)/X(s) = 2s/(s² +2s+1).

(a) Obtain the ordinary differential equation with input x(t) and output y(t). Approximating the derivatives by differences (let T=1) obtain the difference equation that approximates the differential equation.

(b) Let the input be a constant source, so that x[n]=u[n], and let the initial conditions for the difference equation be zero. Solve the difference equation using the Z-transform.

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