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Relationship Between Circular Motion and Waves

Relationship Between Circular Motion and Waves
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2019-04-11 19:18
CircleVectorTrigonometry
This example illustrates the relationship between circular motion and waves. By constructing circular motion geometrically, we can intuitively understand the formation of waves. Key mathematical concepts include circles, trigonometric functions, and vectors. GeoGebra commands used include Circle, Point, Rotate, Angle, Segment, etc. Suitable for high school physics and mathematics education.

GeoGebra Commands & Parameters

  1. Circle(O, B) → c
  2. Point(c) → C
  3. Rotate(C, θ, O) → P
  4. Angle(C, O, P) → α
  5. Segment(O, P) → a
  6. Segment(O, C) → b
  7. OrthogonalLine(C, b) → d
  8. Point(d) → A
  9. OrthogonalLine(A, d) → e
  10. OrthogonalLine(P, e) → f
  11. Intersect(f, e) → Q
  12. Line(C, O) → g
  13. Intersect(c, g) → D, E
  14. Segment(C, E) → h
  15. Midpoint(C, A) → F
  16. Mirror(F, A) → F'
  17. Mirror(A, F') → A'
  18. Mirror(F', A') → F''
  19. Mirror(A', F'') → A''
  20. Mirror(F'', A'') → F'''
  21. Mirror(A'', F''') → A'''
  22. Mirror(F''', A''') → G
  23. Mirror(A''', G) → H
  24. OrthogonalLine(F', d) → i
  25. OrthogonalLine(A', d) → j
  26. OrthogonalLine(F'', d) → k
  27. OrthogonalLine(A'', d) → l
  28. OrthogonalLine(F''', d) → m
  29. OrthogonalLine(A''', d) → n
  30. OrthogonalLine(G, d) → p
  31. OrthogonalLine(H, d) → q
  32. Rotate(P, ε°, O) → P'_1
  33. Angle(P, O, P'_1) → β
  34. Rotate(P, 2.0 * ε°, O) → P'_2
  35. Angle(P, O, P'_2) → γ
  36. Rotate(P, 3.0 * ε°, O) → P'_3
  37. Angle(P, O, P'_3) → δ
  38. Rotate(P, 4.0 * ε°, O) → P'_4
  39. Angle(P, O, P'_4) → ζ
  40. Rotate(P, 5.0 * ε°, O) → P'_5
  41. Angle(P, O, P'_5) → η
  42. Rotate(P, 6.0 * ε°, O) → P'_6
  43. Angle(P, O, P'_6) → ι
  44. Rotate(P, 7.0 * ε°, O) → P'_7
  45. Angle(P, O, P'_7) → μ
  46. OrthogonalLine(P'_1, i) → r
  47. OrthogonalLine(P'_2, j) → s
  48. OrthogonalLine(P'_3, k) → t
  49. OrthogonalLine(P'_4, l) → a_1
  50. OrthogonalLine(P'_5, m) → b_1
  51. OrthogonalLine(P'_6, n) → c_1
  52. OrthogonalLine(P'_7, q) → e_1
  53. Intersect(r, i) → I
  54. Intersect(s, j) → J
  55. Intersect(t, k) → K
  56. Intersect(a_1, l) → L
  57. Intersect(b_1, m) → M
  58. Intersect(c_1, n) → N
  59. Intersect(e_1, p) → R
  60. Rotate(P, 8.0 * ε°, O) → P'_8
  61. Angle(P, O, P'_8) → κ
  62. OrthogonalLine(P'_8, q) → d_1
  63. Intersect(d_1, q) → S

AI Drawing Prompt Reference

Draw a circle O and take a point C on it. Rotate C around O to form point P. Construct a line segment from C to O, and on the circle, take points D and E. Draw a line segment from C to E, and construct a line d perpendicular to this segment. Through P and d, construct a series of perpendicular lines, and rotate P to form points P'_1 to P'_7, and draw perpendicular lines from these points to d.
The prompt above was compiled from the original drawing commands and is for reference only.