Find the damping ratio and natural frequency for each second-order system shown below and show that the value of the damping ratio conforms to the type of response (underdamped, overdamped, and so on) predicted in that problem. T(s) = 5 (5+3)(8+6)

Required information Obtain the steady-state response of each of the following models, and estimate how long the response will take to reach the steady-state. 6x + 8x = 20us (t), x (0) = 0 The steady-state response is The time taken for the response to reach the steady-state is S.

OBJECTIVE 7-3 SECOND-ORDER CIRCUIT ANALYSIS (SECTS. 7-5, 7-6, 7-7) Given a second-order circuit: (a) Find the circuit differential equation. (b) Find the circuit natural frequencies and the initial condi- tions (if not given). (c) Find the zero-input response. (d) Find the complete response for a step function input. See Examples 7-17, 7-18, 7-20 to 7-23, 7-24, and 7-26 and Exercises 7-25, 7-27, 7-29 to 7-31 and 7-33. S7-37 Find the v(t) that satisfies the following differential equa- tion and initial conditions: dv(t) du(t) di² dt +6- +48u(t)=0, v(0)=0 V, dv(0) dt = 48 V/s

How (As what equivalent values) do the 2 resistors transform into the frequencydomain?