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Chapter 5

Chapter 5. Modeling with Higher-Order Differential Equations. FIGURE 5.1.1 Spring/mass system. FIGURE 5.1.2 Direction below the equilibrium position is positive. FIGURE 5.1.3 A relationship between c 1 > 0, c 2 > 0 and phase angle . FIGURE 5.1.4 Simple harmonic motion.

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Chapter 5

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  1. Chapter 5 Modeling with Higher-Order Differential Equations

  2. FIGURE 5.1.1Spring/mass system

  3. FIGURE 5.1.2Direction below the equilibrium position is positive

  4. FIGURE 5.1.3 A relationship between c1 > 0, c2> 0 and phase angle 

  5. FIGURE 5.1.4Simple harmonic motion

  6. FIGURE 5.1.5 Parallel springs

  7. FIGURE 5.1.6 Springs in series

  8. FIGURE 5.1.7Damping devices

  9. FIGURE 5.1.8 Motion of an overdamped system

  10. FIGURE 5.1.9 Motion of a critically damped system

  11. FIGURE 5.1.10 Motion of an underdampedsystem

  12. FIGURE 5.1.11Overdamped system in Example 3

  13. FIGURE 5.1.12 Critically damped system in Example 4

  14. FIGURE 5.1.13 Oscillatory vertical motion of the support

  15. FIGURE 5.1.14 Graph of solution in (28) of Example 6

  16. FIGURE 5.1.15 Graph of solution in Example 7 for various initial velocities x1

  17. FIGURE 5.1.16Pure resonance

  18. FIGURE 5.1.17LRC-series circuit

  19. FIGURE 5.1.18 Graph for Problem 21

  20. FIGURE 5.1.19 Graph for Problem 22

  21. FIGURE 5.1.20Graph for Problem 23

  22. FIGURE 5.1.21Graph for Problem 24

  23. FIGURE 5.1.22Oscillating support in Problem 39

  24. FIGURE 5.1.23 Beats phenomenon in Problem 45

  25. FIGURE 5.2.1 Deflection of a homogeneous beam

  26. FIGURE 5.2.2 Beams with various end conditions

  27. TABLE 5.2.1

  28. FIGURE 5.2.3 Deflection curve for BVP in Example 1

  29. FIGURE 5.2.4 Graphs of eigenfunctionsyn= sin(nx/L), for n = 1, 2, 3, 4, 5

  30. FIGURE 5.2.5Elastic column buckling under a compressive force

  31. FIGURE 5.2.6 Deflection curves corresponding to compressive forces P1, P2, P3

  32. FIGURE 5.2.7 Rotating string and forces acting on it

  33. FIGURE 5.2.8 Deflection of cantilever beam in Problem 7

  34. FIGURE 5.2.9Deflection of vertical column in Problem 24

  35. FIGURE 5.2.10 Concentric spheres in Problem 29

  36. FIGURE 5.2.11Circular ring in Problem 30

  37. FIGURE 5.2.12Propeller shaft of the battleship USS Missouri

  38. FIGURE 5.3.1Hard and soft springs

  39. FIGURE 5.3.2Numerical solution curves

  40. FIGURE 5.3.3Simple pendulum

  41. FIGURE 5.3.4In Example 2, oscillating pendulum in (b); whirling pendulum in (c)

  42. FIGURE 5.3.5 Shape of hanging telephone wires is a catenary

  43. FIGURE 5.3.6 Distance to rocket is large compared to R.

  44. FIGURE 5.3.7 Chain pulled upward by a constant force in Example 4

  45. FIGURE 5.3.8 Graph of (21) in Example 4

  46. FIGURE 5.3.9 Pursuit curve in Problem 17

  47. FIGURE 5.3.10 Pursuit curve in Problem 18

  48. FIGURE 5.3.11 Ballistic pendulum in Problem 19

  49. FIGURE 5.3.12 Airplane drop in Problem 20

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