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Undamped Forced Oscillations

Undamped Forced Oscillations
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2017-09-19 13:04
FunctionTrigonometryCoordinate Geometry
In collections UQ-Applied Mathematical Analysis
This example demonstrates undamped forced oscillations. Key mathematical concepts include oscillation equations and periodic functions. Using GeoGebra commands such as If, Element, and CurveCartesian, the oscillation curve can be constructed. Suitable for high school physics and mathematics education.

GeoGebra Commands & Parameters

  1. If(ω ≠ ω_0, 1, 2) → index
  2. If(index ≟ 1, (F_0 * cos((ω * x))), (F_0 * cos((ω_0 * x)))) → Force
  3. Element(List, index) → Solution
  4. CurveCartesian((2 * sin((((10 * 2) * π) * (j - y_1) / y_l))) + x(B), j, j, y_1, y_0) → S
  5. Segment(PS, PS + (0, 0.5)) → end
  6. CurveCartesian((2 * sin((((10 * 2) * π) * (j - y_1) / y_l))) + x(B), j, j, y_0, y_1) → Saux
  7. Segment(C1, C2) → Plataform
  8. Vector((0, 0), (0, (3 * Force(t)))) → u
  9. Translate(u, (x(B) - 9, y(B))) → u'
  10. Segment(A, A') → Level
  11. Segment((t, 0), A') → LevelTime
  12. Textfield(a) → InputBox1
  13. Textfield(b) → InputBox2
  14. LaTeX(ω_0, true, true) → text1
  15. Textfield(m) → InputBox3
  16. Textfield(k) → InputBox4
  17. Textfield(F_0) → InputBox5
  18. Textfield(ω) → InputBox6

AI Drawing Prompt Reference

Draw a graph of undamped forced oscillations, including a platform, a force curve, and a horizontal line. The platform consists of two points, one at the origin and another on the x-axis. The force curve is calculated using input parameters F_0, ω, and x. The horizontal line intersects the platform to indicate the oscillation's horizontal position.
The prompt above was compiled from the original drawing commands and is for reference only.