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Ferris Wheel Motion Modeling: Trigonometric Periodicity and Height Change Demo

Ferris Wheel Motion Modeling: Trigonometric Periodicity and Height Change Demo
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2017-05-12 21:23
CircleVectorFunctionTrigonometryGraphing
This example demonstrates the vertical height and angle relationship of a Ferris wheel cabin over time. Core concepts involve trigonometric functions, sine curves, periodic motion, and vector rotation. Construction utilizes GeoGebra commands like Circle, Rotate, and Dilate to build geometric structures, combined with InputBox and Textfield for parameter interaction. Suitable for high school math teaching to explain trigonometric modeling and function graph properties, helping students intuitively understand periodic phenomena.

GeoGebra Commands & Parameters

  1. Circle(B, C) → c
  2. Rotate(A, (((2 * π) * a) * n), B) → A'
  3. Dilate(A, If[0 < a ≤ 1, 1 - a, 0], ((n * s), 0)) → A'_1
  4. Segment(E, A) → h
  5. Textfield(r) → InputBox1
  6. Textfield(n) → InputBox2
  7. Textfield(s) → InputBox3
  8. Segment(B, A') → i
  9. Textfield(j) → InputBox4
  10. Textfield(k) → InputBox5
  11. Textfield(d) → InputBox6
  12. Textfield(r) → InputBox7
  13. Intersect(g, l, (108.78466822792045, 380)) → H
  14. Intersect(q, t) → R
  15. Segment(R, A') → f_1
  16. Segment(D, S) → g_1
  17. Dilate(G, If[0 < o ≤ 1, 1 - o, 0], M) → G'
  18. Segment(G, G') → h_1
  19. Dilate(M, If[1 < o ≤ 2, 2 - o, 0], N) → M'
  20. Segment(M, M') → i_1
  21. Dilate(N, If[2 < o ≤ 3, 3 - o, 0], O) → N'
  22. Segment(N, N') → j_1
  23. Dilate(O, If[3 < o ≤ 4, 4 - o, 0], P) → O'
  24. Segment(O, O') → k_1
  25. Dilate(P, If[4 < o ≤ 5, 5 - o, 0], Q) → P'
  26. Segment(P, P') → l_1
  27. Segment(T, DD) → m_1