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Modeling Simple Pendular Motion with Second Order Differential Equation

Modeling Simple Pendular Motion with Second Order Differential Equation
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2019-11-22 00:44
TrigonometryCalculusGeometric Construction
This example models simple pendular motion with a second order differential equation. Key mathematical concepts include second order differential equations and trigonometry. Using GeoGebra commands such as Circle, Point, Segment, Angle, Vector, Tangent, Intersect, CircleArc, the geometric model of pendular motion is constructed. Suitable for high school mathematics education and students learning calculus.

GeoGebra Commands & Parameters

  1. Circle(FixedPoint, l) → c
  2. Point(c) → A
  3. Segment(FixedPoint, A) → f
  4. Point(eq1) → B
  5. Angle(B, FixedPoint, A) → θ
  6. Vector(A, A - (0, 1)) → u
  7. Tangent(A, c) → g,
  8. Circle(A, sin(θ)) → d
  9. Intersect(d, g, 2) → C
  10. Vector(A, C) → v
  11. Intersect(d, g, 1) → D
  12. Vector(A, D) → w
  13. Vector(C, E) → a
  14. Vector(D, E) → b
  15. Intersect(c, eq1, 2) → F
  16. CircleArc(FixedPoint, A, F) → e
  17. CircleArc(FixedPoint, F, A) → h