Mastering Engineering with Pearson eText -- Standalone Access Card -- for Electrical Engineering: Principles & Applications
7th Edition
ISBN: 9780134486970
Author: Allan R. Hambley
Publisher: PEARSON
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Chapter 4, Problem 4.57P
To determine
The way in which the under damped, over damped and critically damped second order system are identified and the form its complementary solution take.
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a. Compare the performances of the first order system, the overdamped, underdamped and critically damped second order system.
b. Explain how the performances of second order system depend on the damping ratio and the natural frequency.
The dynamic behavior of the second-order system can then bedescribed in terms of two parameters undamped natural frequency anddamping ratio of the system. What is the different value of damping ratio?
What are the pros/cons of a second-order dynamic system? What dynamic property is the preferred in general, underdamped, critically damped or overdamped and why?
Chapter 4 Solutions
Mastering Engineering with Pearson eText -- Standalone Access Card -- for Electrical Engineering: Principles & Applications
Ch. 4 - Suppose we have a capacitance C discharging...Ch. 4 - The dielectric materials used in real capacitors...Ch. 4 - The initial voltage across the capacitor shown in...Ch. 4 - A 100F capacitance is initially charged to 1000 V....Ch. 4 - At t = 0, a charged 10{ F capacitance is connected...Ch. 4 - At time t1 , a capacitance C is charged to a...Ch. 4 - Given an initially charged capacitance that begins...Ch. 4 - The initial voltage across the capacitor shown in...Ch. 4 - In physics, the half-life is often used to...Ch. 4 - We know that a 50F capacitance is charged to an...
Ch. 4 - We know that the capacitor shown in Figure P4.11...Ch. 4 - The purchasing power P of a certain unit of...Ch. 4 - Derive an expression for vC(t) in the circuit of...Ch. 4 - Suppose that at t= 0, we connect an uncharged 10 F...Ch. 4 - Suppose we have a capacitance C that is charged to...Ch. 4 - A person shuffling across a dry carpet can be...Ch. 4 - Prob. 4.17PCh. 4 - Consider the circuit shown in Figure P4.18. Prior...Ch. 4 - List the steps for dc steady-state analysis of RLC...Ch. 4 - Explain why we replace capacitances with open...Ch. 4 - Solve for the steady-state values of i1, i2, and...Ch. 4 - Consider the circuit shown in Figure P4.22. What...Ch. 4 - In the circuit of Figure P4.23, the switch is in...Ch. 4 - The circuit shown in Figure P4.24 has been set up...Ch. 4 - Solve for the steady-state values of i1 , i2, i3,...Ch. 4 - The circuit shown in Figure P4.26 is operating in...Ch. 4 - Prob. 4.27PCh. 4 - Consider the circuit of Figure P4.28 in which the...Ch. 4 - For the circuit shown in Figure P4.29, the switch...Ch. 4 - Consider the circuit of Figure P4.30 in which the...Ch. 4 - Give the expression for the time constant of a...Ch. 4 - A circuit consists of switches that open or close...Ch. 4 - The circuit shown in Figure P4.33 is operating in...Ch. 4 - Consider the circuit shown in Figure P4.34. The...Ch. 4 - Repeat Problem P4.34 given iL(0)=0A .Ch. 4 - Real inductors have series resistance associated...Ch. 4 - Determine expressions for and sketch is(t) to...Ch. 4 - For the circuit shown in Figure P4.38,, find an...Ch. 4 - The circuit shown in Figure P4.39 is operating in...Ch. 4 - Consider the circuit shown in Figure P4.40. A...Ch. 4 - Due to components not shown in the figure, the...Ch. 4 - The switch shown in Figure P4.42 has been closed...Ch. 4 - Determine expressions for and sketch vR(t) to...Ch. 4 - What are the steps in solving a circuit having a...Ch. 4 - Prob. 4.45PCh. 4 - Solve for vC(t) for t > 0 in the circuit of Figure...Ch. 4 - Solve for v(t) for t > 0 in the circuit of Figure...Ch. 4 - Prob. 4.48PCh. 4 - Consider the circuit shown inFigure P4.49. The...Ch. 4 - Consider the circuit shown in Figure P4.50. The...Ch. 4 - The voltage source shown in Figure P4.51 is called...Ch. 4 - Determine the form of the particular solution for...Ch. 4 - Determine the form of the particular solution for...Ch. 4 - Prob. 4.54PCh. 4 - Prob. 4.55PCh. 4 - How can first-or second-order circuits be...Ch. 4 - Prob. 4.57PCh. 4 - Prob. 4.58PCh. 4 - Prob. 4.59PCh. 4 - Sketch a step response for a second-order system...Ch. 4 - A dc source is connected to a series RLC circuit...Ch. 4 - Repeat Problem P4.61 for R = 40 .Ch. 4 - Repeat Problem P4.61 for R = 20 .Ch. 4 - Prob. 4.64PCh. 4 - Repeat Problem P4.64 for R=50 .Ch. 4 - Repeat Problem P4.64 for R=500 .Ch. 4 - Solve for i(t) for t > 0 in the circuit of Figure...Ch. 4 - Prob. 4.68PCh. 4 - Prob. 4.69PCh. 4 - Prob. 4.70PCh. 4 - Use MATLAB to derive an expression for vc(t)in the...Ch. 4 - Prob. 4.72PCh. 4 - Consider the circuit shown in FigureP4.50 in which...Ch. 4 - Prob. 4.74PCh. 4 - Prob. 4.75PCh. 4 - Use MATLAB to solve for the mesh currents in the...Ch. 4 - The switch m the circuit shown in Figure T4.1 is...Ch. 4 - Prob. 4.2PTCh. 4 - Consider the circuit shown in Figure T4.3. Figure...Ch. 4 - Consider the circuit shown in Figure T4.4 in which...Ch. 4 - Write the MATLAB commands to obtain the solution...
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- Explore the challenges and advancements in modeling nonlinear and time-varying systems, and their significance in real-world applications.arrow_forwardProblem 2: a. Compare the performances of the first order system, the overdamped, underdamped and critically damped second order system. b. Explain how the performances of second order system depend on the damping ratio and the natural frequency.arrow_forwardIs the circuit currently in steady-state or transient condition? Justify your answer.arrow_forward
- Given the second order electrical network shown in the following figure:It is known that the switch shown, T, is initially open and that its state changes to closed in theinstant t = 0. If it is assumed that the circuit has reached the stable state before the action of said switch:a) Find the value of inductance L so that the given network exhibits a critically responsemuffled.b) For the damping conditions of the previous part, determine, as a function of time, the expression for the voltage, v (t), for all t> 0.arrow_forwardExplain the First-Order Systems and its Applications?arrow_forward1. What effect does increasingg the system gain have upon a SECOND ORDER STEADY-STATE ERROR? a) It has no effect on the system steady state error b) Its effect depends on the system characteristic equation c) It will decrease the steady state error d) It will increase the steady state error e) It depends on the tupe of system 2. Does a stable first order system have overshoot? 3. If the damping ration of a s.o.s is greater than 1, are types are the poles and where are they located on the plane? please answer all 3 carefullyarrow_forward
- Solve for the steady-state values of iR in milliampere (mA), and VC in Volts (V) for the circuit shown below, assuming that the circuit has been connected for a long time.arrow_forwardPlease see attachment and please show handwritten work! A system is described by the differential equation: Determine the values of the natural frequency, damping ratio and the dampednatural frequency for this system. This system is: _____Undamped _____Underdamped _____Critically Damped _____Overdamped *** Please see attachment, and please show handwritten work! Thank you!arrow_forwarda) What should be the K value for the closed system to be critically damped? b) In what range should the K value be in order for the given system to be underdamped and overdamped.arrow_forward
- What are the application of load forecasting in neural network based methods.arrow_forwardIt is known that the switch shown, T, is initially open and then it closed in theinstant t = 0. If it is assumed that the circuit has reached the stable state before the action of said switch:1.1. Determine the value of the capacitance of capacitor C so that the given circuit is critically damped.1.2. For the damping conditions of the previous part, find the expression for the current, i (t), forall t> 0.arrow_forwardGive an example of a second-order, constant-coefficient, homogeneous equation with non-real roots of the characteristic equation. Write down the linear system that corresponds to it. Can you find an example of an interconnected system of two tanks that is described by this system? Explain. Then solve the system.arrow_forward
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