This is completed downloadable of First Course in Differential Equations Modeling and Simulation 2nd Smith Solution Manual

Product Details:

ISBN-13: 978-1482257229

Author: Carlos A. Smith (Author), Scott W. Campbell (Author)

A First Course in Differential Equations, Modeling, and Simulation shows how differential equations arise from applying basic physical principles and experimental observations to engineering systems. Avoiding overly theoretical explanations, the textbook also discusses classical and Laplace transform methods for obtaining the analytical solution of differential equations. In addition, the authors explain how to solve sets of differential equations where analytical solutions cannot easily be obtained.

Incorporating valuable suggestions from mathematicians and mathematics professors, the Second Edition:

Expands the chapter on classical solutions of ordinary linear differential equations to include additional methods
Increases coverage of response of first- and second-order systems to a full, stand-alone chapter to emphasize its importance
Includes new examples of applications related to chemical reactions, environmental engineering, biomedical engineering, and biotechnology
Contains new exercises that can be used as projects and answers to many of the end-of-chapter problems
Features new end-of-chapter problems and updates throughout

Thus, A First Course in Differential Equations, Modeling, and Simulation, Second Edition provides students with a practical understanding of how to apply differential equations in modern engineering and science.

Table of Content:

1.1 An Introductory Example
FIGURE 1.1 Mixing tank.
FIGURE 1.2 Response of level in tank.
1.2 Differential Equations
1.2.1 Initial and Boundary Conditions
FIGURE 1.3 Graph of Equation 1.18.
FIGURE 1.4 RLC circuit.
1.2.2 Ordinary and Partial Differential Equations
FIGURE 1.5 Well-insulated pipe.
1.3 Modeling
1.4 Forcing Functions
FIGURE 1.6 Step change in flow of stream 1.
FIGURE 1.7 Forcing function for Example 1.1.
Example 1.1
Example 1.2
FIGURE 1.8 Forcing function for Example 1.2.
Example 1.3
Example 1.4
1.5 Book Objectives
1.6 Summary
PROBLEMS
FIGURE P1.1 Graphs for Problem 1.1.
FIGURE P1.2 Thrust curve for a model rocket engine.
2 Objects in a Gravitational Field
2.1 An Example
FIGURE 2.1 Object held aboveground.
2.2 Antidifferentiation: Technique for Solving First-Order Ordinary Differential Equations
2.3 Back to Section 2.1
2.4 Another Example
2.5 Separation of Variables: Technique for Solving First -Order Ordinary Differential Equations
2.6 Back to Section 2.4
2.7 Equations, Unknowns, and Degrees of Freedom
2.8 Partial Fraction Expansion
2.8.1 Unrepeated Real Roots
2.8.2 Repeated Real Roots
Example 2.1
Example 2.2
2.9 Summary
PROBLEMS
3 Classical Solutions of Ordinary Linear Differential Equations
3.1 Examples of Differential Equations
3.1.1 Bioengineering: Chapter 8
3.1.2 Mechanical Translational: Chapter 6
3.1.3 Fluid System: Chapter 8
FIGURE 3.1 Mass–spring–dashpot system.
FIGURE 3.2 Liquid level.
3.1.4 Thermal System: Chapter 9
FIGURE 3.3 Heat transfer from the sole plate of an electric iron.
3.1.5 Electrical Circuit: Chapter 10
FIGURE 3.4 Electrical circuit.
3.2 Definition of a Linear Differential Equation
Example 3.1
3.3 Integrating Factor Method
Example 3.2
Example 3.3
Example 3.4
3.3.1 Development of the Integrating Factor Method
3.4 Solution of Homogeneous Differential Equations
3.4.1 Characteristic Equation
Example 3.5
3.4.2 Roots of the Characteristic Equation
DEVELOPMENT OF EQUATION 3.25
3.4.3 Qualitative System Response
FIGURE 3.5 Roots of characteristic equation.
Example 3.6
Example 3.7
3.5 Solution of Nonhomogeneous Differential Equations
3.5.1 Homogeneous Solution (Natural Response) and Nonhomogeneous Solution (Forced Response)
3.5.2 Undetermined Coefficients
TABLE 3.1 Solutions for the Particular Solution
Example 3.8
Example 3.9
Example 3.10
Example 3.11
Example 3.12
Example 3.13
Example 3.14
Example 3.15
3.5.3 Multiple Forcing Functions
FIGURE 3.6 Cart with multiple forcing functions.
3.6 Variation of Parameters
3.6.1 Second-Order Systems
Example 3.16
Example 3.17
Example 3.18
CRAMER’S RULE
3.6.2 Higher-Order Systems
3.7 Handling Nonlinearities and Variable Coefficients
3.7.1 Taylor Series
Example 3.19
3.7.2 Linearization of Nonlinear Differential Equations
FIGURE 3.7 Linear approximation.
Example 3.20
FIGURE 3.8 Comparison of actual and linearized models.
FIGURE 3.9 Comparison of actual and new linearized models.
Example 3.21
Example 3.22
FIGURE 3.10 Comparison of actual and linearized models.
FIGURE 3.11 Comparison of actual and linearized models.
3.8 Transient and Final Responses
FIGURE 3.12 Graphs of (a) Equation 3.41 and (b) Equation 3.49.
3.9 Summary
PROBLEMS
FIGURE P3.1 Roots for Problem 3.6
FIGURE P3.2 Water treatment basins for Problem 3.8.
FIGURE P3.3 Spring–mass–dashpot system for Problem 3.11.
FIGURE P3.4 Spring–mass–dashpot system for Problem 3.14.
FIGURE P3.5 Mechanical system for Problem 3.16.
FIGURE P3.6 Mechanical system for Problem 3.17.
FIGURE P3.7 Mechanical system for Problem 3.18.
FIGURE P3.8 Mechanical system for Problem 3.19.
FIGURE P3.9 Electrical circuit for Problem 3.20.
FIGURE P3.10 Electrical circuit for Problem 3.21.
FIGURE P3.11 Electrical circuit for Problem 3.22.
FIGURE P3.12 Electrical circuit for Problem 3.25.
FIGURE P3.13 Electrical circuit for Problem 3.26.
FIGURE P3.14 Electrical circuit for Problem 3.27.
4 Laplace Transforms
4.1 Definition of the Laplace Transform
Example 4.1
FIGURE 4.1 Common input signals: (a) unit step function, (b) pulse, (c) unit impulse function, and (d) sine wave.
TABLE 4.1 Laplace Transforms of Common Functions
4.2 Properties and Theorems of the Laplace Transform
4.2.1 Linearity Property
4.2.2 Real Differentiation Theorem
4.2.3 Real Integration Theorem
4.2.4 Real Translation Theorem
FIGURE 4.2 Function delayed in time is zero for all times less than the time delay t0.
4.2.5 Final Value Theorem
4.2.6 Complex Differentiation Theorem
4.2.7 Complex Translation Theorem
4.2.8 Initial Value Theorem
Example 4.2
Example 4.3
Example 4.4
4.3 Solution of Differential Equations Using Laplace Transform
4.3.1 Inversion by Partial Fraction Expansion
4.3.1.1 Unrepeated Real Roots
Example 4.5
4.3.1.2 Repeated Real Roots
Example 4.6
4.3.1.3 Complex Roots
4.3.1.3.1 First-Order Expansion
4.3.1.3.2 Second-Order Expansion
COMPLETING THE SQUARE
Example 4.7
Example 4.8
Example 4.9
Example 4.10
Example 4.11
Example 4.12
Example 4.13
Example 4.14
Example 4.15
4.3.2 Handling Time Delays
Example 4.16
FIGURE 4.3 Input functions for Example 4.16. (a) Delayed unit step, u(t − 1). (b) Staircase of unit steps.
4.4 Transfer Functions
4.5 Algebraic Manipulations Using Laplace Transforms
FIGURE 4.4 Frictionless carts with an external force.
4.6 Deviation Variables
FIGURE 4.5 Mass–spring–dashpot system.
Example 4.17
Example 4.18
FIGURE 4.6 Electrical circuit.
4.7 Summary
PROBLEMS
5 Response of First- and Second-Order Systems
5.1 First-Order Systems
5.1.1 Step Function Input
FIGURE 5.1 Response of a first-order system to a step change in input.
TABLE 5.1 First-Order Step Response
5.1.2 Sinusoidal Function Input
5.1.3 Transfer Function
5.2 Second-Order Systems
5.2.1 Step Function Input
5.2.1.1 Types of Stable Systems
FIGURE 5.2 Response of second-order system to a step change in forcing function.
5.2.1.2 Underdamped Response
FIGURE 5.3 Second-order underdamped response (ζ = 0.5) of step input.
TABLE 5.2 Second-Order Underdamped Step Response
FIGURE 5.4 Effect of damping ratio on the second-order underdamped step response.
FIGURE 5.5 Undamped response.
5.2.1.3 Undamped Response
5.2.2 Sinusoidal Function Input
5.2.3 Transfer Function
5.3 Examples
FIGURE 5.6 Mass–spring–dashpot system.
Example 5.1
Example 5.2
FIGURE 5.7 Electrical circuit.
Example 5.3
FIGURE 5.8 Information for Example 5.3.
Example 5.4
FIGURE 5.9 Information for Example 5.4.
5.4 Some Concluding Remarks
5.5 Summary
PROBLEMS
FIGURE P5.1 Schematic for Problem 5.1.
FIGURE P5.2 Electrical circuit for Problem 5.2.
FIGURE P5.3 Information for Problem 5.3.
FIGURE P5.4 Mechanical system for Problem 5.7.
6 Mechanical Systems: Translational
6.1 Mechanical Law, System Components, and Forces
6.1.1 Mechanical Law
FIGURE 6.1 Springs.
6.1.2 System Components
6.1.2.1 Springs
FIGURE 6.2 Forces generated by springs.
FIGURE 6.3 (a) Ideal and (b) real springs.
6.1.2.2 Dashpots (Pistons or Dampers)
FIGURE 6.4 Spring–mass system showing dashpot.
6.1.2.3 Ideal Pulley
FIGURE 6.5 Mechanical system showing a pulley.
FIGURE 6.6 (a) Dry friction force between two surfaces. (b) Fluid friction force between two surfaces.
6.1.3 Forces
FIGURE 6.7 Demonstration of the negative sign in Equation 6.4.
6.2 Types of Systems
6.2.1 Undamped System
FIGURE 6.8 Mass–spring system.
FIGURE 6.9 Response for undamped system—with and without resonance.
6.2.2 Damped System
FIGURE 6.10 Spring–mass system.
6.3 D’Alembert’s Principle and Free Body Diagrams
FIGURE 6.11 Mass–spring–dashpot system.
FIGURE 6.12 Free body diagram of the system shown in Figure 6.11.
FIGURE 6.13 Response of cart shown in Figure 6.11.
6.4 Examples
FIGURE 6.14 System consisting of two blocks.
FIGURE 6.15 Displacement of blocks after applying force.
Example 6.1
FIGURE 6.16 Frictionless carts with an external force.
FIGURE 6.17 Response of carts.
FIGURE 6.18 Free body diagrams for carts in Figure 6.16.
FIGURE 6.19 Free body diagrams for carts in Figure 6.16.
Example 6.2
FIGURE 6.20 Cart with friction and an external force.
FIGURE 6.21 Free body diagrams for carts of Figure 6.20.
FIGURE 6.22 Free body diagrams for carts of Figure 6.20.
Example 6.3
FIGURE 6.23 Two blocks with friction.
6.5 Vertical Systems
Example 6.4
FIGURE 6.24 Vertical mechanical system.
FIGURE 6.25 Displacement of system of Example 6.4.
6.6 Summary
PROBLEMS
FIGURE P6.1 Mechanical system for Problem 6.1.
FIGURE P6.2 Mechanical system for Problem 6.2.
FIGURE P6.3 Mechanical system for Problem 6.3.
FIGURE P6.4 Mechanical system for Problem 6.4.
FIGURE P6.5 Mechanical system for Problem 6.5.
FIGURE P6.6 Mechanical system for Problem 6.6.
FIGURE P6.7 Mechanical system for Problem 6.7.
FIGURE P6.8 Mechanical system for Problem 6.8.
FIGURE P6.9 Mechanical system for Problem 6.9.
FIGURE P6.10 Mechanical system for Problem 6.10.
FIGURE P6.11 Mechanical system for Problem 6.11.
FIGURE P6.12 Mechanical system for Problem 6.12.
FIGURE P6.13 Mechanical system for Problem 6.13.
FIGURE P6.14 Mechanical system for Problem 6.14.
FIGURE P6.15 Mechanical system for Problem 6.15.
FIGURE P6.16 Mechanical system for Problem 6.16.
FIGURE P6.17 Mechanical system for Problem 6.17.
FIGURE P6.18 Cart system for Problem 6.18.
FIGURE P6.19 Block system for Problem 6.19.
FIGURE P6.20 Block system for Problem 6.20.
FIGURE P6.21 Block system for Problem 6.21.
FIGURE P6.22 Block system for Problem 6.22.
7 Mechanical Systems: Rotational
7.1 Mechanical Law, Moment of Inertia, and Torque
FIGURE 7.1 Angular position θ.
TABLE 7.1 Analogous Relations between Translational and Rotational Systems
7.1.1 Mass Moment of Inertia
Example 7.1
FIGURE 7.2 Rotation of a slender bar and enlarged view of volume element.
7.1.2 Torque
Example 7.2
FIGURE 7.3 Moment arm d between axis of rotation A and the line of action C of a force F.
FIGURE 7.4 A pendulum comprised of a slender rod.
FIGURE 7.5 Moment arm evaluation (a) and free body diagram (b) for the pendulum of Example 7.2.
FIGURE 7.6 Comparison of analytical solution of linearized Equation 7.20 to numerical solution of Equation 7.17 for (a) θ0 = 30° and (b) θ0 = 90°.
7.2 Torsion Springs
FIGURE 7.7 Torsion bar.
Example 7.3
FIGURE 7.8 System of two rotating masses and two torsion springs.
FIGURE 7.9 Free body diagrams of the masses in Example 7.3.
7.3 Rotational Damping
FIGURE 7.10 Damping in a rotational system.
Example 7.4
FIGURE 7.11 Rotational system of Example 7.4.
FIGURE 7.12 Free body diagrams for Example 7.4.
FIGURE 7.13 Solution to Equations 7.32 and 7.33 using parameters given in part (b).
7.4 Gears
FIGURE 7.14 (a) Two gears and (b) partial FBD showing the contact force fC.
Example 7.5
FIGURE 7.15 Geared elements of Example 7.5.
FIGURE 7.16 Free body diagrams for the gears of Example 7.5.
7.5 Systems with Rotational and Translational Elements
Example 7.6
FIGURE 7.17 Drum and mass system of Example 7.6.
FIGURE 7.18 Free body diagrams for Example 7.6.
FIGURE 7.19 Velocity (a) and spring stretch (b) versus time for the system of Example 7.6.
7.6 Summary
PROBLEMS
FIGURE P7.1 Disks of mass m, radius R, and length L for parts (a) and (b) and the suggested volume element.
FIGURE P7.2 Pendulum made of a slender bar with friction at the pin.
FIGURE P7.3 Torsion spring with damping.
FIGURE P7.4 Single torsion spring of Problem 7.4.
FIGURE P7.5 Wheel and pulley system of Problem 7.5.
FIGURE P7.6 Viscous coupler.
FIGURE P7.7 Centrifugal clutch.
FIGURE P7.8 Viscous coupler of Problem 7.8.
FIGURE P7.9 System of two masses and torsion springs for Problem 7.9.
FIGURE P7.10 Mass and rotating drum of Problem 7.10.
FIGURE P7.11 System of translating and rotating masses of Problem 7.11.
FIGURE P7.12 System of Problem 7.12.
FIGURE P7.13 Single-speed bicycle.
FIGURE P7.14 Scotch yoke linkage.
FIGURE P7.15 Winch of Problem 7.15.
FIGURE P7.16 Spool transfer system of Problem 7.16.
FIGURE P7.17 Disk and two masses of Problem 7.17.
FIGURE P7.18 System of Problem 7.18.
8 Mass Balances
8.1 Conservation of Mass
FIGURE 8.1 Generic system.
8.1.1 Multicomponent Systems
8.1.2 Types of Processes
8.2 Flow Rates and Concentrations
8.3 Elements and Experimental Facts
8.3.1 Flow Element
FIGURE 8.2 Process valve.
FIGURE 8.3 Control valve.
8.3.2 Liquid Service
FIGURE 8.4 Liquid level.
8.3.3 Gas Service
8.4 Examples
Example 8.1
Example 8.2
FIGURE 8.5 Mixing tank.
Example 8.3
Example 8.4
FIGURE 8.6 Gas system.
8.5 Expressions for Mass Transport and Chemical Reactions
8.5.1 Mass Transport
FIGURE 8.7 Mass transfer of component A from phase I to phase II.
8.5.2 Chemical Reactions
FIGURE 8.8 Chemical reactor.
8.5.2.1 Half-Life
8.5.3 Batch Processes
FIGURE 8.9 Closed system.
8.5.3.1 Batch Separation
FIGURE 8.10 Batch reactor.
8.5.3.2 Batch Reactor
8.6 Additional Examples
Example 8.5
FIGURE 8.11 Water treatment basins.
Example 8.6
FIGURE 8.12 Benzene concentration in basins.
Example 8.7
FIGURE 8.13 Batch reactor for Example 8.7.
Example 8.8
FIGURE 8.14 Water filter.
8.7 Application to Bioengineering Processes
FIGURE 8.15 Body divided into compartments for modeling purposes.
8.7.1 Compartmental Modeling
FIGURE 8.16 Disappearance of a protein (solute) in blood.
FIGURE 8.17 Transfer of a solute between two compartments.
8.7.2 Biological Reactions
Example 8.9
FIGURE 8.18 Single compartment for Example 8.9.
Example 8.10
FIGURE 8.19 Response of an antibiotic.
Example 8.11
FIGURE 8.20 Antibiotic in blood.
8.7.3 Fermentation
FIGURE 8.21 Substrate concentration versus time.
Example 8.12
Example 8.13
8.8 Final Comments
8.9 Summary
References
PROBLEMS
FIGURE P8.1 Tank for Problem 8.1.
FIGURE P8.2 Process for Problem 8.2.
FIGURE P8.3 Tank for Problem 8.3.
FIGURE P8.4 Tank for Problem 8.4.
FIGURE P8.5 Tanks for Problem 8.5.
FIGURE P8.6 Tank for Problem 8.9.
FIGURE P8.7 Mixing tank for Problem 8.10.
Steady-State Values
FIGURE P8.8 Tank system for Problem 8.11.
FIGURE P8.9 Storage tank for Problem 8.14.
FIGURE P8.10 Tray of a distillation column for Problem 8.15.
FIGURE P8.11 Process tank with pump manipulating exit stream.
FIGURE P8.12 Compartments representing muscle and blood.
FIGURE P8.13 Chemical hood for Problem 8.25.
9 Thermal Systems
9.1 Conservation of Energy
9.2 Modes of Heat Transfer
9.3 Conduction
FIGURE 9.1 Heat conduction through a plate.
9.4 Convection
FIGURE 9.2 Convection of heat from an object of surface temperature T and surface area A to a fluid at temperature Tf.
9.5 Conduction and Convection in Series
FIGURE 9.3 Heat transfer by convection and conduction.
9.6 Accumulated or Stored Energy
9.7 Some Examples
Example 9.1: Convective Heat Transfer
FIGURE 9.4 Graph of Equation 9.26 with two different values of α.
Example 9.2: Heating of a Liquid in a Jacketed, Stirred Vessel
FIGURE 9.5 Heating of water in a jacketed, stirred vessel.
Example 9.3: Convective Heat Transfer with Internal Generation
FIGURE 9.6 Heat transfer from the sole plate of an electric iron.
FIGURE 9.7 Temperature profile for the sole plate showing ultimate temperature and time to reach 100°C.
9.8 Heat Transfer in a Flow System
FIGURE 9.8 Heating of a vessel with inlet and outlet flows.
Example 9.4: Heating of a Vessel with Inflows and Outflows
9.9 Thermal Effects in a Reactive System
FIGURE 9.9 Solution to Equations 9.75 and 9.76 for an adiabatic batch reactor using given parameter values.
9.10 Boundary Value Problems in Heat Transfer
Example 9.5: Temperature Profile and Heat Flow in Wire Insulation
FIGURE 9.10 An insulated wire.
FIGURE 9.11 Expanded view of the insulation showing the chosen volume element.
Example 9.6: Steady-State Temperature Profile in a Sphere with Internal Heat Generation
FIGURE 9.12 Spherical pellet and selected volume element.
FIGURE 9.13 Temperature versus radial position for the sphere of Example 9.6. The lumped parameter approximation is represented by the solid line and the full solutions by the dashed curves. The long dashes, medium dashes, and short dashes correspond to Biot numbers of 1.0, 0.1, and 0.02, respectively.
Example 9.7: Steady-State Heat Transfer from an Extended Surface
FIGURE 9.14 Heat transfer from an extended surface.
FIGURE 9.15 Percent difference between the heat flow from an extended, infinitely long circular rod calculated assuming two-dimensional conduction and that calculated assuming one-dimensional conduction.
9.11 Summary
PROBLEMS
FIGURE P9.1 Cooled water bath of Problem 9.8.
FIGURE P9.2 Heated bath of Problem 9.9.
10 Electrical Systems
10.1 Some Definitions and Conventions
FIGURE 10.1 Schematic of ideal voltage and current sources.
10.2 Electrical Laws, Components, and Initial Conditions
10.2.1 Electrical Laws
FIGURE 10.2 Closed-loop electrical circuit.
FIGURE 10.3 Electrical node.
10.2.2 Electrical Components
FIGURE 10.4 Resistor.
FIGURE 10.5 Capacitor.
FIGURE 10.6 Tank with flexible membrane.
FIGURE 10.7 Capacitor becoming an open circuit at steady state.
FIGURE 10.8 Inductor.
FIGURE 10.9 Inductor becoming a simple conductor at steady state.
10.2.3 Initial Conditions
FIGURE 10.10 Electrical circuit.
FIGURE 10.11 Voltage and current behavior.
10.3 Examples of Electrical Circuits
Example 10.1
FIGURE 10.12 RC circuit.
FIGURE 10.13 RC circuit at initial steady state.
FIGURE 10.14 Response of RC circuit shown in Figure 10.12.
Example 10.2
FIGURE 10.15 RL circuit.
FIGURE 10.16 RL circuit at initial steady state.
Example 10.3
FIGURE 10.17 RLC circuit.
Example 10.4
FIGURE 10.18 Circuit for Example 10.4.
FIGURE 10.19 Circuit for Example 10.4, part (a).
FIGURE 10.20 Circuit for Example 10.4, part (b).
10.3.1 Undamped Circuit (Natural Frequency and Resonance)
FIGURE 10.21 LC circuits.
FIGURE 10.22 Responses of LC circuits.
FIGURE 10.23 LC circuits with some amount of resistance.
10.4 Additional Examples
Example 10.5
FIGURE 10.24 Electrical circuit for Example 10.5.
Example 10.6
FIGURE 10.25 Electrical circuit for Example 10.6.
FIGURE 10.26 Electrical circuit for Example 10.6 showing open circuit.
NODAL METHOD
FIGURE 10.27 Electrical circuit showing information for the nodal method.
MESH METHOD
FIGURE 10.28 Electric circuit showing meshes.
Example 10.7
FIGURE 10.29 Electrical circuit.
FIGURE 10.30 Redraw of Figure 10.29.
FIGURE 10.31 Redraw of Figure 10.30.
Example 10.8
FIGURE 10.32 Circuits for Example 10.8.
FIGURE 10.33 Charging and discharging of the capacitor in Figure 10.29a.
10.5 Energy and Power
FIGURE 10.34 Electrical component.
10.5.1 Resistors
FIGURE 10.35 Resistor.
10.5.2 Capacitors
10.5.3 Inductors
Example 10.9
FIGURE 10.36 RLC circuit.
FIGURE 10.37 Power and energy responses of components in Figure 10.36.
FIGURE 10.38 Circuits for t ≥ 2 s.
FIGURE 10.39 Voltages and currents for circuits in Figure 10.36.
FIGURE 10.40 Energy contained in the circuits of Figure 10.38.
Example 10.10
FIGURE 10.41 Electrical circuit.
FIGURE 10.42 Chip temperature.
10.6 RC Circuits as Filters
FIGURE 10.43 Ideal filters. (a) High-pass filter. (b) Low-pass filter.
FIGURE 10.44 RC circuit.
10.6.1 High-Pass Filter
FIGURE 10.45 Voltage drop across a resistor in an RC circuit.
FIGURE 10.46 Performance of an RC circuit as a high-pass filter.
10.6.2 Low-Pass Filter
FIGURE 10.47 Voltage drop across a capacitor in an RC circuit.
FIGURE 10.48 Performance of an RC circuit as a low-pass filter.
FIGURE 10.49 Performance of an RC circuit as a low-pass filter and as a high-pass filter. (a) Input signal to circuit. (b) Output of high-pass filter. (c) Output of low-pass filter.
10.7 Summary
PROBLEMS
FIGURE P10.1 Circuit for Problem 10.1.
FIGURE P10.2 Circuit for Problem 10.2.
FIGURE P10.3 Circuit for Problem 10.3.
FIGURE P10.4 Circuit for Problem 10.4.
FIGURE P10.5 Circuit for Problem 10.5.
FIGURE P10.6 Circuit for Problem 10.6.
FIGURE P10.7 Circuit for Problem 10.7.
FIGURE P10.8 Circuit for Problem 10.8.
FIGURE P10.9 Circuit for Problem 10.9.
FIGURE P10.10 Circuit for Problem 10.10.
FIGURE P10.11 Circuit for Problem 10.11.
FIGURE P10.12 Circuit for Problem 10.12.
FIGURE P10.13 Circuit for Problem 10.13.
FIGURE P10.14 Circuit for Problem 10.14.
FIGURE P10.15 Circuit for Problem 10.15.
FIGURE P10.16 Circuit for Problem 10.16.
FIGURE P10.17 Circuit for Problem 10.17.
FIGURE P10.18 Circuit for Problem 10.18.
FIGURE P10.19 Circuit for Problem 10.19.
FIGURE P10.20 Circuit for Problem 10.20.
FIGURE P10.21 Circuit for Problem 10.21.
FIGURE P10.22 Circuit for Problem 10.22.
FIGURE P10.23 Circuit for Problem 10.23.
FIGURE P10.24 Circuit for Problem 10.24.
FIGURE P10.25 Circuit for Problem 10.25.
FIGURE P10.26 Circuit for Problem 10.26.
FIGURE P10.27 (a) Circuit for Problem 10.27a. (b) Circuit for Problem 10.27b.
FIGURE P10.28 Circuit for Problem 10.28.
11 Numerical Simulation
11.1 Numerical Solution of Differential Equations
TABLE 11.1 Numerical Solution of Equation 11.1 for Tf = 200, T0 = 25, and α = 0.1
11.2 Euler’s Method for First-Order Ordinary Differential Equations
Example 11.1
11.3 Euler’s Method for Second-Order Ordinary Differential Equations
Example 11.2
11.4 Step Size
FIGURE 11.1 Illustration of the effect of step size in Euler’s method using the differential equation of Example 11.1.
11.5 More Sophisticated Methods
11.6 Representation of Differential Equations by Block Diagrams
11.6.1 Basic Blocks
11.6.2 Guidelines for Constructing Block Diagrams
Example 11.3
11.6.3 Some Additional Examples
Example 11.4
Example 11.5
Example 11.6
11.6.4 Some Additional Source Blocks
11.6.4.1 Step Block
11.6.4.2 Sine Wave
11.7 Additional Examples
Example 11.7
FIGURE 11.2 Diagram for the simulation of Equations 6.36 and 6.37.
FIGURE 11.3 Response of the carts of Example 11.7.
FIGURE 11.4 Difference (%) between the responses obtained from the analytical solution and simulation. (a) Cart 1 and (b) Cart 2.
Example 11.8
FIGURE 11.5 Block diagram for the simulation of Equation 8.32.
FIGURE 11.6 Response of the level in the tank.
FIGURE 11.7 Response of the level to three consecutive changes in inlet flow of 2 m3/min.
Example 11.9
FIGURE 11.8 Electrical circuit.
FIGURE 11.9 Simulation (block diagram) of Equation 11.22b.
FIGURE 11.10 Response of voltage drop vD.
FIGURE 11.11 Block diagram for Equations 11.17 through 11.21.
11.8 Summary
Reference
PROBLEMS
FIGURE P11.1 Thrust curve for rocket engine of Problem 11.10.
FIGURE P11.2 Shock absorber of Problem 11.15.
FIGURE P11.3 Speed bump of Problem 11.15.
FIGURE P11.4 Mechanical system for Problem 11.17.
FIGURE P11.5 Mechanical system for Problem 11.18.
FIGURE P11.6 Waste disposal tank with three pumps.
Back Matter
Answers to Selected Problems
Chapter 1
Chapter 2
Chapter 3
Chapter 4
Chapter 5
Chapter 6
Chapter 7
Chapter 8
Chapter 9
Chapter 10
Chapter 11
Index