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Vector Rotation Animation of Metronome: Exploring Periodic Motion

Vector Rotation Animation of Metronome: Exploring Periodic Motion
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2024-10-11 16:41
VectorSequenceTransformationGeometric ConstructionSlider Animation
In collections El dominio del Tiempo (cinemática intuitiva)
This example demonstrates a classic metronome's periodic swinging motion through a rotating pendulum. Core mathematical concepts include vector rotation transformations, parametric representation of circular motion, and periodic function characteristics. Construction highlights: Circle commands create the dial and swing trajectory, Rotate commands implement pendulum rotation animation, CircleArc commands draw arc paths, Sequence and Zip commands generate continuous motion sequences, UnitOrthogonalVector calculates orthogonal vectors, Line and Segment build the pendulum rod structure, with Slider animation controls for adjustable speed. Suitable for secondary school mathematics teaching on trigonometry, vector rotation, parametric equations, and pre-university periodic motion visualization.

GeoGebra Commands & Parameters

  1. Circle(O, l) → c
  2. Rotate(O + (0, (-l)), -6°, O) → A
  3. Rotate(O + (0, (-l)), 6°, O) → A'
  4. CircleArc(O, A, A') → arc
  5. Point(arc) → M
  6. Segment(O, M) → r
  7. UnitOrthogonalVector(r) → n
  8. Line(M, gt) → i
  9. Segment(O, O + (0.8 * UnitVector[Vector[M, O]])) → f
  10. Circle(O - (0.2, 0.04), 0.02) → e
  11. Circle(O - (0.2, 0.04), 0.08) → d
  12. UnitOrthogonalVector(f) → nM
  13. Segment(M' - (0.05 * UnitVector[O - M]) - (0.05 * nM), M' - (0.05 * UnitVector[O - M]) + (0.05 * nM)) → h
  14. Zip(4 + (0.6 / 168 * (208 - a)), a, m1) → m2
  15. Zip(B + (5, 0.3 + (208 - a) / 16), a, m3) → marcas3
  16. Zip(Text[a, b], a, tempos, b, marcas3) → l1
  17. Sequence(Polygon[B + (0, 0.5 + (208 - m1(k)) / 16), B + (7, 0.5 + (208 - m1(k)) / 16), B + (7, 0.5 + (208 - m1(k + 1)) / 16), B + (0, 0.5 + (208 - m1(k + 1)) / 16)], k, 1, Length[m1] - 1) → pol
  18. Zip(Segment[B + (0, 0.5 + (208 - a) / 16), B + (2.4, 0.5 + (208 - a) / 16)], a, m1) → marcas2
  19. Zip(Segment[(x(O), a) - (0.05 * UnitVector[O - M]) - (0.05 * (-1, 0)), (x(O), a) - (0.05 * UnitVector[O - M]) + (0.05 * (-1, 0))], a, m2) → marcas1

AI Drawing Prompt Reference

Create a 2D diagram with a circular dial centered at O with radius l. Construct two pendulum end positions by rotating an initial offset point around O to symmetric angles, then draw the arc between these two endpoints on the circle. Choose a point M on the arc and connect O to M with a segment representing the pendulum rod. Determine the direction orthogonal to the rod to place small perpendicular offset marks near M. Add small decorative circles for dial/tick emphasis and include vertical segmented annotations aligned with the tick locations to suggest periodic motion. Arrange everything to resemble a metronome swing, with a slider intended to control the animation speed.
The prompt above was compiled from the original drawing commands and is for reference only.