The RLC circuit described in Problem 28 and shown in Figure P28 has the following differential equation model:

 

Use the Laplace transform method to solve for the unit-step response of υ0(t) for zero initial conditions, where C = 10^-5 F and L = 5 , 10^-3 H.

For the first case (a broadband filter), R = 1000 Ω. For the second case (a narrowband lter), R = 10 Ω. Compare the step responses of the two cases.

LC, + RCv, + v, RCv,(1)