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First Course in Differential Equations Modeling and Simulation 2nd Smith Solution Manual

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First Course in Differential Equations Modeling and Simulation 2nd Smith Solution Manual

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

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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. 1.1 An Introductory Example
  2. FIGURE 1.1 Mixing tank.
  3. FIGURE 1.2 Response of level in tank.
  4. 1.2 Differential Equations
  5. 1.2.1 Initial and Boundary Conditions
  6. FIGURE 1.3 Graph of Equation 1.18.
  7. FIGURE 1.4 RLC circuit.
  8. 1.2.2 Ordinary and Partial Differential Equations
  9. FIGURE 1.5 Well-insulated pipe.
  10. 1.3 Modeling
  11. 1.4 Forcing Functions
  12. FIGURE 1.6 Step change in flow of stream 1.
  13. FIGURE 1.7 Forcing function for Example 1.1.
  14. Example 1.1
  15. Example 1.2
  16. FIGURE 1.8 Forcing function for Example 1.2.
  17. Example 1.3
  18. Example 1.4
  19. 1.5 Book Objectives
  20. 1.6 Summary
  21. PROBLEMS
  22. FIGURE P1.1 Graphs for Problem 1.1.
  23. FIGURE P1.2 Thrust curve for a model rocket engine.
  24. 2 Objects in a Gravitational Field
  25. 2.1 An Example
  26. FIGURE 2.1 Object held aboveground.
  27. 2.2 Antidifferentiation: Technique for Solving First-Order Ordinary Differential Equations
  28. 2.3 Back to Section 2.1
  29. 2.4 Another Example
  30. 2.5 Separation of Variables: Technique for Solving First -Order Ordinary Differential Equations
  31. 2.6 Back to Section 2.4
  32. 2.7 Equations, Unknowns, and Degrees of Freedom
  33. 2.8 Partial Fraction Expansion
  34. 2.8.1 Unrepeated Real Roots
  35. 2.8.2 Repeated Real Roots
  36. Example 2.1
  37. Example 2.2
  38. 2.9 Summary
  39. PROBLEMS
  40. 3 Classical Solutions of Ordinary Linear Differential Equations
  41. 3.1 Examples of Differential Equations
  42. 3.1.1 Bioengineering: Chapter 8
  43. 3.1.2 Mechanical Translational: Chapter 6
  44. 3.1.3 Fluid System: Chapter 8
  45. FIGURE 3.1 Mass–spring–dashpot system.
  46. FIGURE 3.2 Liquid level.
  47. 3.1.4 Thermal System: Chapter 9
  48. FIGURE 3.3 Heat transfer from the sole plate of an electric iron.
  49. 3.1.5 Electrical Circuit: Chapter 10
  50. FIGURE 3.4 Electrical circuit.
  51. 3.2 Definition of a Linear Differential Equation
  52. Example 3.1
  53. 3.3 Integrating Factor Method
  54. Example 3.2
  55. Example 3.3
  56. Example 3.4
  57. 3.3.1 Development of the Integrating Factor Method
  58. 3.4 Solution of Homogeneous Differential Equations
  59. 3.4.1 Characteristic Equation
  60. Example 3.5
  61. 3.4.2 Roots of the Characteristic Equation
  62. DEVELOPMENT OF EQUATION 3.25
  63. 3.4.3 Qualitative System Response
  64. FIGURE 3.5 Roots of characteristic equation.
  65. Example 3.6
  66. Example 3.7
  67. 3.5 Solution of Nonhomogeneous Differential Equations
  68. 3.5.1 Homogeneous Solution (Natural Response) and Nonhomogeneous Solution (Forced Response)
  69. 3.5.2 Undetermined Coefficients
  70. TABLE 3.1 Solutions for the Particular Solution
  71. Example 3.8
  72. Example 3.9
  73. Example 3.10
  74. Example 3.11
  75. Example 3.12
  76. Example 3.13
  77. Example 3.14
  78. Example 3.15
  79. 3.5.3 Multiple Forcing Functions
  80. FIGURE 3.6 Cart with multiple forcing functions.
  81. 3.6 Variation of Parameters
  82. 3.6.1 Second-Order Systems
  83. Example 3.16
  84. Example 3.17
  85. Example 3.18
  86. CRAMER’S RULE
  87. 3.6.2 Higher-Order Systems
  88. 3.7 Handling Nonlinearities and Variable Coefficients
  89. 3.7.1 Taylor Series
  90. Example 3.19
  91. 3.7.2 Linearization of Nonlinear Differential Equations
  92. FIGURE 3.7 Linear approximation.
  93. Example 3.20
  94. FIGURE 3.8 Comparison of actual and linearized models.
  95. FIGURE 3.9 Comparison of actual and new linearized models.
  96. Example 3.21
  97. Example 3.22
  98. FIGURE 3.10 Comparison of actual and linearized models.
  99. FIGURE 3.11 Comparison of actual and linearized models.
  100. 3.8 Transient and Final Responses
  101. FIGURE 3.12 Graphs of (a) Equation 3.41 and (b) Equation 3.49.
  102. 3.9 Summary
  103. PROBLEMS
  104. FIGURE P3.1 Roots for Problem 3.6
  105. FIGURE P3.2 Water treatment basins for Problem 3.8.
  106. FIGURE P3.3 Spring–mass–dashpot system for Problem 3.11.
  107. FIGURE P3.4 Spring–mass–dashpot system for Problem 3.14.
  108. FIGURE P3.5 Mechanical system for Problem 3.16.
  109. FIGURE P3.6 Mechanical system for Problem 3.17.
  110. FIGURE P3.7 Mechanical system for Problem 3.18.
  111. FIGURE P3.8 Mechanical system for Problem 3.19.
  112. FIGURE P3.9 Electrical circuit for Problem 3.20.
  113. FIGURE P3.10 Electrical circuit for Problem 3.21.
  114. FIGURE P3.11 Electrical circuit for Problem 3.22.
  115. FIGURE P3.12 Electrical circuit for Problem 3.25.
  116. FIGURE P3.13 Electrical circuit for Problem 3.26.
  117. FIGURE P3.14 Electrical circuit for Problem 3.27.
  118. 4 Laplace Transforms
  119. 4.1 Definition of the Laplace Transform
  120. Example 4.1
  121. FIGURE 4.1 Common input signals: (a) unit step function, (b) pulse, (c) unit impulse function, and (d) sine wave.
  122. TABLE 4.1 Laplace Transforms of Common Functions
  123. 4.2 Properties and Theorems of the Laplace Transform
  124. 4.2.1 Linearity Property
  125. 4.2.2 Real Differentiation Theorem
  126. 4.2.3 Real Integration Theorem
  127. 4.2.4 Real Translation Theorem
  128. FIGURE 4.2 Function delayed in time is zero for all times less than the time delay t0.
  129. 4.2.5 Final Value Theorem
  130. 4.2.6 Complex Differentiation Theorem
  131. 4.2.7 Complex Translation Theorem
  132. 4.2.8 Initial Value Theorem
  133. Example 4.2
  134. Example 4.3
  135. Example 4.4
  136. 4.3 Solution of Differential Equations Using Laplace Transform
  137. 4.3.1 Inversion by Partial Fraction Expansion
  138. 4.3.1.1 Unrepeated Real Roots
  139. Example 4.5
  140. 4.3.1.2 Repeated Real Roots
  141. Example 4.6
  142. 4.3.1.3 Complex Roots
  143. 4.3.1.3.1 First-Order Expansion
  144. 4.3.1.3.2 Second-Order Expansion
  145. COMPLETING THE SQUARE
  146. Example 4.7
  147. Example 4.8
  148. Example 4.9
  149. Example 4.10
  150. Example 4.11
  151. Example 4.12
  152. Example 4.13
  153. Example 4.14
  154. Example 4.15
  155. 4.3.2 Handling Time Delays
  156. Example 4.16
  157. FIGURE 4.3 Input functions for Example 4.16. (a) Delayed unit step, u(t − 1). (b) Staircase of unit steps.
  158. 4.4 Transfer Functions
  159. 4.5 Algebraic Manipulations Using Laplace Transforms
  160. FIGURE 4.4 Frictionless carts with an external force.
  161. 4.6 Deviation Variables
  162. FIGURE 4.5 Mass–spring–dashpot system.
  163. Example 4.17
  164. Example 4.18
  165. FIGURE 4.6 Electrical circuit.
  166. 4.7 Summary
  167. PROBLEMS
  168. 5 Response of First- and Second-Order Systems
  169. 5.1 First-Order Systems
  170. 5.1.1 Step Function Input
  171. FIGURE 5.1 Response of a first-order system to a step change in input.
  172. TABLE 5.1 First-Order Step Response
  173. 5.1.2 Sinusoidal Function Input
  174. 5.1.3 Transfer Function
  175. 5.2 Second-Order Systems
  176. 5.2.1 Step Function Input
  177. 5.2.1.1 Types of Stable Systems
  178. FIGURE 5.2 Response of second-order system to a step change in forcing function.
  179. 5.2.1.2 Underdamped Response
  180. FIGURE 5.3 Second-order underdamped response (ζ = 0.5) of step input.
  181. TABLE 5.2 Second-Order Underdamped Step Response
  182. FIGURE 5.4 Effect of damping ratio on the second-order underdamped step response.
  183. FIGURE 5.5 Undamped response.
  184. 5.2.1.3 Undamped Response
  185. 5.2.2 Sinusoidal Function Input
  186. 5.2.3 Transfer Function
  187. 5.3 Examples
  188. FIGURE 5.6 Mass–spring–dashpot system.
  189. Example 5.1
  190. Example 5.2
  191. FIGURE 5.7 Electrical circuit.
  192. Example 5.3
  193. FIGURE 5.8 Information for Example 5.3.
  194. Example 5.4
  195. FIGURE 5.9 Information for Example 5.4.
  196. 5.4 Some Concluding Remarks
  197. 5.5 Summary
  198. PROBLEMS
  199. FIGURE P5.1 Schematic for Problem 5.1.
  200. FIGURE P5.2 Electrical circuit for Problem 5.2.
  201. FIGURE P5.3 Information for Problem 5.3.
  202. FIGURE P5.4 Mechanical system for Problem 5.7.
  203. 6 Mechanical Systems: Translational
  204. 6.1 Mechanical Law, System Components, and Forces
  205. 6.1.1 Mechanical Law
  206. FIGURE 6.1 Springs.
  207. 6.1.2 System Components
  208. 6.1.2.1 Springs
  209. FIGURE 6.2 Forces generated by springs.
  210. FIGURE 6.3 (a) Ideal and (b) real springs.
  211. 6.1.2.2 Dashpots (Pistons or Dampers)
  212. FIGURE 6.4 Spring–mass system showing dashpot.
  213. 6.1.2.3 Ideal Pulley
  214. FIGURE 6.5 Mechanical system showing a pulley.
  215. FIGURE 6.6 (a) Dry friction force between two surfaces. (b) Fluid friction force between two surfaces.
  216. 6.1.3 Forces
  217. FIGURE 6.7 Demonstration of the negative sign in Equation 6.4.
  218. 6.2 Types of Systems
  219. 6.2.1 Undamped System
  220. FIGURE 6.8 Mass–spring system.
  221. FIGURE 6.9 Response for undamped system—with and without resonance.
  222. 6.2.2 Damped System
  223. FIGURE 6.10 Spring–mass system.
  224. 6.3 D’Alembert’s Principle and Free Body Diagrams
  225. FIGURE 6.11 Mass–spring–dashpot system.
  226. FIGURE 6.12 Free body diagram of the system shown in Figure 6.11.
  227. FIGURE 6.13 Response of cart shown in Figure 6.11.
  228. 6.4 Examples
  229. FIGURE 6.14 System consisting of two blocks.
  230. FIGURE 6.15 Displacement of blocks after applying force.
  231. Example 6.1
  232. FIGURE 6.16 Frictionless carts with an external force.
  233. FIGURE 6.17 Response of carts.
  234. FIGURE 6.18 Free body diagrams for carts in Figure 6.16.
  235. FIGURE 6.19 Free body diagrams for carts in Figure 6.16.
  236. Example 6.2
  237. FIGURE 6.20 Cart with friction and an external force.
  238. FIGURE 6.21 Free body diagrams for carts of Figure 6.20.
  239. FIGURE 6.22 Free body diagrams for carts of Figure 6.20.
  240. Example 6.3
  241. FIGURE 6.23 Two blocks with friction.
  242. 6.5 Vertical Systems
  243. Example 6.4
  244. FIGURE 6.24 Vertical mechanical system.
  245. FIGURE 6.25 Displacement of system of Example 6.4.
  246. 6.6 Summary
  247. PROBLEMS
  248. FIGURE P6.1 Mechanical system for Problem 6.1.
  249. FIGURE P6.2 Mechanical system for Problem 6.2.
  250. FIGURE P6.3 Mechanical system for Problem 6.3.
  251. FIGURE P6.4 Mechanical system for Problem 6.4.
  252. FIGURE P6.5 Mechanical system for Problem 6.5.
  253. FIGURE P6.6 Mechanical system for Problem 6.6.
  254. FIGURE P6.7 Mechanical system for Problem 6.7.
  255. FIGURE P6.8 Mechanical system for Problem 6.8.
  256. FIGURE P6.9 Mechanical system for Problem 6.9.
  257. FIGURE P6.10 Mechanical system for Problem 6.10.
  258. FIGURE P6.11 Mechanical system for Problem 6.11.
  259. FIGURE P6.12 Mechanical system for Problem 6.12.
  260. FIGURE P6.13 Mechanical system for Problem 6.13.
  261. FIGURE P6.14 Mechanical system for Problem 6.14.
  262. FIGURE P6.15 Mechanical system for Problem 6.15.
  263. FIGURE P6.16 Mechanical system for Problem 6.16.
  264. FIGURE P6.17 Mechanical system for Problem 6.17.
  265. FIGURE P6.18 Cart system for Problem 6.18.
  266. FIGURE P6.19 Block system for Problem 6.19.
  267. FIGURE P6.20 Block system for Problem 6.20.
  268. FIGURE P6.21 Block system for Problem 6.21.
  269. FIGURE P6.22 Block system for Problem 6.22.
  270. 7 Mechanical Systems: Rotational
  271. 7.1 Mechanical Law, Moment of Inertia, and Torque
  272. FIGURE 7.1 Angular position θ.
  273. TABLE 7.1 Analogous Relations between Translational and Rotational Systems
  274. 7.1.1 Mass Moment of Inertia
  275. Example 7.1
  276. FIGURE 7.2 Rotation of a slender bar and enlarged view of volume element.
  277. 7.1.2 Torque
  278. Example 7.2
  279. FIGURE 7.3 Moment arm d between axis of rotation A and the line of action C of a force F.
  280. FIGURE 7.4 A pendulum comprised of a slender rod.
  281. FIGURE 7.5 Moment arm evaluation (a) and free body diagram (b) for the pendulum of Example 7.2.
  282. 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°.
  283. 7.2 Torsion Springs
  284. FIGURE 7.7 Torsion bar.
  285. Example 7.3
  286. FIGURE 7.8 System of two rotating masses and two torsion springs.
  287. FIGURE 7.9 Free body diagrams of the masses in Example 7.3.
  288. 7.3 Rotational Damping
  289. FIGURE 7.10 Damping in a rotational system.
  290. Example 7.4
  291. FIGURE 7.11 Rotational system of Example 7.4.
  292. FIGURE 7.12 Free body diagrams for Example 7.4.
  293. FIGURE 7.13 Solution to Equations 7.32 and 7.33 using parameters given in part (b).
  294. 7.4 Gears
  295. FIGURE 7.14 (a) Two gears and (b) partial FBD showing the contact force fC.
  296. Example 7.5
  297. FIGURE 7.15 Geared elements of Example 7.5.
  298. FIGURE 7.16 Free body diagrams for the gears of Example 7.5.
  299. 7.5 Systems with Rotational and Translational Elements
  300. Example 7.6
  301. FIGURE 7.17 Drum and mass system of Example 7.6.
  302. FIGURE 7.18 Free body diagrams for Example 7.6.
  303. FIGURE 7.19 Velocity (a) and spring stretch (b) versus time for the system of Example 7.6.
  304. 7.6 Summary
  305. PROBLEMS
  306. FIGURE P7.1 Disks of mass m, radius R, and length L for parts (a) and (b) and the suggested volume element.
  307. FIGURE P7.2 Pendulum made of a slender bar with friction at the pin.
  308. FIGURE P7.3 Torsion spring with damping.
  309. FIGURE P7.4 Single torsion spring of Problem 7.4.
  310. FIGURE P7.5 Wheel and pulley system of Problem 7.5.
  311. FIGURE P7.6 Viscous coupler.
  312. FIGURE P7.7 Centrifugal clutch.
  313. FIGURE P7.8 Viscous coupler of Problem 7.8.
  314. FIGURE P7.9 System of two masses and torsion springs for Problem 7.9.
  315. FIGURE P7.10 Mass and rotating drum of Problem 7.10.
  316. FIGURE P7.11 System of translating and rotating masses of Problem 7.11.
  317. FIGURE P7.12 System of Problem 7.12.
  318. FIGURE P7.13 Single-speed bicycle.
  319. FIGURE P7.14 Scotch yoke linkage.
  320. FIGURE P7.15 Winch of Problem 7.15.
  321. FIGURE P7.16 Spool transfer system of Problem 7.16.
  322. FIGURE P7.17 Disk and two masses of Problem 7.17.
  323. FIGURE P7.18 System of Problem 7.18.
  324. 8 Mass Balances
  325. 8.1 Conservation of Mass
  326. FIGURE 8.1 Generic system.
  327. 8.1.1 Multicomponent Systems
  328. 8.1.2 Types of Processes
  329. 8.2 Flow Rates and Concentrations
  330. 8.3 Elements and Experimental Facts
  331. 8.3.1 Flow Element
  332. FIGURE 8.2 Process valve.
  333. FIGURE 8.3 Control valve.
  334. 8.3.2 Liquid Service
  335. FIGURE 8.4 Liquid level.
  336. 8.3.3 Gas Service
  337. 8.4 Examples
  338. Example 8.1
  339. Example 8.2
  340. FIGURE 8.5 Mixing tank.
  341. Example 8.3
  342. Example 8.4
  343. FIGURE 8.6 Gas system.
  344. 8.5 Expressions for Mass Transport and Chemical Reactions
  345. 8.5.1 Mass Transport
  346. FIGURE 8.7 Mass transfer of component A from phase I to phase II.
  347. 8.5.2 Chemical Reactions
  348. FIGURE 8.8 Chemical reactor.
  349. 8.5.2.1 Half-Life
  350. 8.5.3 Batch Processes
  351. FIGURE 8.9 Closed system.
  352. 8.5.3.1 Batch Separation
  353. FIGURE 8.10 Batch reactor.
  354. 8.5.3.2 Batch Reactor
  355. 8.6 Additional Examples
  356. Example 8.5
  357. FIGURE 8.11 Water treatment basins.
  358. Example 8.6
  359. FIGURE 8.12 Benzene concentration in basins.
  360. Example 8.7
  361. FIGURE 8.13 Batch reactor for Example 8.7.
  362. Example 8.8
  363. FIGURE 8.14 Water filter.
  364. 8.7 Application to Bioengineering Processes
  365. FIGURE 8.15 Body divided into compartments for modeling purposes.
  366. 8.7.1 Compartmental Modeling
  367. FIGURE 8.16 Disappearance of a protein (solute) in blood.
  368. FIGURE 8.17 Transfer of a solute between two compartments.
  369. 8.7.2 Biological Reactions
  370. Example 8.9
  371. FIGURE 8.18 Single compartment for Example 8.9.
  372. Example 8.10
  373. FIGURE 8.19 Response of an antibiotic.
  374. Example 8.11
  375. FIGURE 8.20 Antibiotic in blood.
  376. 8.7.3 Fermentation
  377. FIGURE 8.21 Substrate concentration versus time.
  378. Example 8.12
  379. Example 8.13
  380. 8.8 Final Comments
  381. 8.9 Summary
  382. References
  383. PROBLEMS
  384. FIGURE P8.1 Tank for Problem 8.1.
  385. FIGURE P8.2 Process for Problem 8.2.
  386. FIGURE P8.3 Tank for Problem 8.3.
  387. FIGURE P8.4 Tank for Problem 8.4.
  388. FIGURE P8.5 Tanks for Problem 8.5.
  389. FIGURE P8.6 Tank for Problem 8.9.
  390. FIGURE P8.7 Mixing tank for Problem 8.10.
  391. Steady-State Values
  392. FIGURE P8.8 Tank system for Problem 8.11.
  393. FIGURE P8.9 Storage tank for Problem 8.14.
  394. FIGURE P8.10 Tray of a distillation column for Problem 8.15.
  395. FIGURE P8.11 Process tank with pump manipulating exit stream.
  396. FIGURE P8.12 Compartments representing muscle and blood.
  397. FIGURE P8.13 Chemical hood for Problem 8.25.
  398. 9 Thermal Systems
  399. 9.1 Conservation of Energy
  400. 9.2 Modes of Heat Transfer
  401. 9.3 Conduction
  402. FIGURE 9.1 Heat conduction through a plate.
  403. 9.4 Convection
  404. FIGURE 9.2 Convection of heat from an object of surface temperature T and surface area A to a fluid at temperature Tf.
  405. 9.5 Conduction and Convection in Series
  406. FIGURE 9.3 Heat transfer by convection and conduction.
  407. 9.6 Accumulated or Stored Energy
  408. 9.7 Some Examples
  409. Example 9.1: Convective Heat Transfer
  410. FIGURE 9.4 Graph of Equation 9.26 with two different values of α.
  411. Example 9.2: Heating of a Liquid in a Jacketed, Stirred Vessel
  412. FIGURE 9.5 Heating of water in a jacketed, stirred vessel.
  413. Example 9.3: Convective Heat Transfer with Internal Generation
  414. FIGURE 9.6 Heat transfer from the sole plate of an electric iron.
  415. FIGURE 9.7 Temperature profile for the sole plate showing ultimate temperature and time to reach 100°C.
  416. 9.8 Heat Transfer in a Flow System
  417. FIGURE 9.8 Heating of a vessel with inlet and outlet flows.
  418. Example 9.4: Heating of a Vessel with Inflows and Outflows
  419. 9.9 Thermal Effects in a Reactive System
  420. FIGURE 9.9 Solution to Equations 9.75 and 9.76 for an adiabatic batch reactor using given parameter values.
  421. 9.10 Boundary Value Problems in Heat Transfer
  422. Example 9.5: Temperature Profile and Heat Flow in Wire Insulation
  423. FIGURE 9.10 An insulated wire.
  424. FIGURE 9.11 Expanded view of the insulation showing the chosen volume element.
  425. Example 9.6: Steady-State Temperature Profile in a Sphere with Internal Heat Generation
  426. FIGURE 9.12 Spherical pellet and selected volume element.
  427. 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.
  428. Example 9.7: Steady-State Heat Transfer from an Extended Surface
  429. FIGURE 9.14 Heat transfer from an extended surface.
  430. 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.
  431. 9.11 Summary
  432. PROBLEMS
  433. FIGURE P9.1 Cooled water bath of Problem 9.8.
  434. FIGURE P9.2 Heated bath of Problem 9.9.
  435. 10 Electrical Systems
  436. 10.1 Some Definitions and Conventions
  437. FIGURE 10.1 Schematic of ideal voltage and current sources.
  438. 10.2 Electrical Laws, Components, and Initial Conditions
  439. 10.2.1 Electrical Laws
  440. FIGURE 10.2 Closed-loop electrical circuit.
  441. FIGURE 10.3 Electrical node.
  442. 10.2.2 Electrical Components
  443. FIGURE 10.4 Resistor.
  444. FIGURE 10.5 Capacitor.
  445. FIGURE 10.6 Tank with flexible membrane.
  446. FIGURE 10.7 Capacitor becoming an open circuit at steady state.
  447. FIGURE 10.8 Inductor.
  448. FIGURE 10.9 Inductor becoming a simple conductor at steady state.
  449. 10.2.3 Initial Conditions
  450. FIGURE 10.10 Electrical circuit.
  451. FIGURE 10.11 Voltage and current behavior.
  452. 10.3 Examples of Electrical Circuits
  453. Example 10.1
  454. FIGURE 10.12 RC circuit.
  455. FIGURE 10.13 RC circuit at initial steady state.
  456. FIGURE 10.14 Response of RC circuit shown in Figure 10.12.
  457. Example 10.2
  458. FIGURE 10.15 RL circuit.
  459. FIGURE 10.16 RL circuit at initial steady state.
  460. Example 10.3
  461. FIGURE 10.17 RLC circuit.
  462. Example 10.4
  463. FIGURE 10.18 Circuit for Example 10.4.
  464. FIGURE 10.19 Circuit for Example 10.4, part (a).
  465. FIGURE 10.20 Circuit for Example 10.4, part (b).
  466. 10.3.1 Undamped Circuit (Natural Frequency and Resonance)
  467. FIGURE 10.21 LC circuits.
  468. FIGURE 10.22 Responses of LC circuits.
  469. FIGURE 10.23 LC circuits with some amount of resistance.
  470. 10.4 Additional Examples
  471. Example 10.5
  472. FIGURE 10.24 Electrical circuit for Example 10.5.
  473. Example 10.6
  474. FIGURE 10.25 Electrical circuit for Example 10.6.
  475. FIGURE 10.26 Electrical circuit for Example 10.6 showing open circuit.
  476. NODAL METHOD
  477. FIGURE 10.27 Electrical circuit showing information for the nodal method.
  478. MESH METHOD
  479. FIGURE 10.28 Electric circuit showing meshes.
  480. Example 10.7
  481. FIGURE 10.29 Electrical circuit.
  482. FIGURE 10.30 Redraw of Figure 10.29.
  483. FIGURE 10.31 Redraw of Figure 10.30.
  484. Example 10.8
  485. FIGURE 10.32 Circuits for Example 10.8.
  486. FIGURE 10.33 Charging and discharging of the capacitor in Figure 10.29a.
  487. 10.5 Energy and Power
  488. FIGURE 10.34 Electrical component.
  489. 10.5.1 Resistors
  490. FIGURE 10.35 Resistor.
  491. 10.5.2 Capacitors
  492. 10.5.3 Inductors
  493. Example 10.9
  494. FIGURE 10.36 RLC circuit.
  495. FIGURE 10.37 Power and energy responses of components in Figure 10.36.
  496. FIGURE 10.38 Circuits for t ≥ 2 s.
  497. FIGURE 10.39 Voltages and currents for circuits in Figure 10.36.
  498. FIGURE 10.40 Energy contained in the circuits of Figure 10.38.
  499. Example 10.10
  500. FIGURE 10.41 Electrical circuit.
  501. FIGURE 10.42 Chip temperature.
  502. 10.6 RC Circuits as Filters
  503. FIGURE 10.43 Ideal filters. (a) High-pass filter. (b) Low-pass filter.
  504. FIGURE 10.44 RC circuit.
  505. 10.6.1 High-Pass Filter
  506. FIGURE 10.45 Voltage drop across a resistor in an RC circuit.
  507. FIGURE 10.46 Performance of an RC circuit as a high-pass filter.
  508. 10.6.2 Low-Pass Filter
  509. FIGURE 10.47 Voltage drop across a capacitor in an RC circuit.
  510. FIGURE 10.48 Performance of an RC circuit as a low-pass filter.
  511. 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.
  512. 10.7 Summary
  513. PROBLEMS
  514. FIGURE P10.1 Circuit for Problem 10.1.
  515. FIGURE P10.2 Circuit for Problem 10.2.
  516. FIGURE P10.3 Circuit for Problem 10.3.
  517. FIGURE P10.4 Circuit for Problem 10.4.
  518. FIGURE P10.5 Circuit for Problem 10.5.
  519. FIGURE P10.6 Circuit for Problem 10.6.
  520. FIGURE P10.7 Circuit for Problem 10.7.
  521. FIGURE P10.8 Circuit for Problem 10.8.
  522. FIGURE P10.9 Circuit for Problem 10.9.
  523. FIGURE P10.10 Circuit for Problem 10.10.
  524. FIGURE P10.11 Circuit for Problem 10.11.
  525. FIGURE P10.12 Circuit for Problem 10.12.
  526. FIGURE P10.13 Circuit for Problem 10.13.
  527. FIGURE P10.14 Circuit for Problem 10.14.
  528. FIGURE P10.15 Circuit for Problem 10.15.
  529. FIGURE P10.16 Circuit for Problem 10.16.
  530. FIGURE P10.17 Circuit for Problem 10.17.
  531. FIGURE P10.18 Circuit for Problem 10.18.
  532. FIGURE P10.19 Circuit for Problem 10.19.
  533. FIGURE P10.20 Circuit for Problem 10.20.
  534. FIGURE P10.21 Circuit for Problem 10.21.
  535. FIGURE P10.22 Circuit for Problem 10.22.
  536. FIGURE P10.23 Circuit for Problem 10.23.
  537. FIGURE P10.24 Circuit for Problem 10.24.
  538. FIGURE P10.25 Circuit for Problem 10.25.
  539. FIGURE P10.26 Circuit for Problem 10.26.
  540. FIGURE P10.27 (a) Circuit for Problem 10.27a. (b) Circuit for Problem 10.27b.
  541. FIGURE P10.28 Circuit for Problem 10.28.
  542. 11 Numerical Simulation
  543. 11.1 Numerical Solution of Differential Equations
  544. TABLE 11.1 Numerical Solution of Equation 11.1 for Tf = 200, T0 = 25, and α = 0.1
  545. 11.2 Euler’s Method for First-Order Ordinary Differential Equations
  546. Example 11.1
  547. 11.3 Euler’s Method for Second-Order Ordinary Differential Equations
  548. Example 11.2
  549. 11.4 Step Size
  550. FIGURE 11.1 Illustration of the effect of step size in Euler’s method using the differential equation of Example 11.1.
  551. 11.5 More Sophisticated Methods
  552. 11.6 Representation of Differential Equations by Block Diagrams
  553. 11.6.1 Basic Blocks
  554. 11.6.2 Guidelines for Constructing Block Diagrams
  555. Example 11.3
  556. 11.6.3 Some Additional Examples
  557. Example 11.4
  558. Example 11.5
  559. Example 11.6
  560. 11.6.4 Some Additional Source Blocks
  561. 11.6.4.1 Step Block
  562. 11.6.4.2 Sine Wave
  563. 11.7 Additional Examples
  564. Example 11.7
  565. FIGURE 11.2 Diagram for the simulation of Equations 6.36 and 6.37.
  566. FIGURE 11.3 Response of the carts of Example 11.7.
  567. FIGURE 11.4 Difference (%) between the responses obtained from the analytical solution and simulation. (a) Cart 1 and (b) Cart 2.
  568. Example 11.8
  569. FIGURE 11.5 Block diagram for the simulation of Equation 8.32.
  570. FIGURE 11.6 Response of the level in the tank.
  571. FIGURE 11.7 Response of the level to three consecutive changes in inlet flow of 2 m3/min.
  572. Example 11.9
  573. FIGURE 11.8 Electrical circuit.
  574. FIGURE 11.9 Simulation (block diagram) of Equation 11.22b.
  575. FIGURE 11.10 Response of voltage drop vD.
  576. FIGURE 11.11 Block diagram for Equations 11.17 through 11.21.
  577. 11.8 Summary
  578. Reference
  579. PROBLEMS
  580. FIGURE P11.1 Thrust curve for rocket engine of Problem 11.10.
  581. FIGURE P11.2 Shock absorber of Problem 11.15.
  582. FIGURE P11.3 Speed bump of Problem 11.15.
  583. FIGURE P11.4 Mechanical system for Problem 11.17.
  584. FIGURE P11.5 Mechanical system for Problem 11.18.
  585. FIGURE P11.6 Waste disposal tank with three pumps.
  586. Back Matter
  587. Answers to Selected Problems
  588. Chapter 1
  589. Chapter 2
  590. Chapter 3
  591. Chapter 4
  592. Chapter 5
  593. Chapter 6
  594. Chapter 7
  595. Chapter 8
  596. Chapter 9
  597. Chapter 10
  598. Chapter 11
  599. Index

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