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Undamped Spring

Undamped Spring
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2021-09-01 11:33
FunctionTrigonometryCalculus
In collections MATH1052-edX
This example demonstrates the motion of an undamped spring. Key mathematical concepts include differential equations and trigonometric functions. Using GeoGebra commands such as If, Segment, Textfield, and CurveCartesian, the motion trajectory of the spring can be constructed. Suitable for high school physics and mathematics courses.

GeoGebra Commands & Parameters

  1. If(ylength < 0, CurveCartesian[(2 * sin((((10 * 2) * π) * (t - y_1) / (y_0 - y_1)))) + x(A2), t, t, y_0, y_1], CurveCartesian[(2 * sin((((10 * 2) * π) * (t - y_1) / (y_0 - y_1)))) + x(A2), t, t, y_1, y_0]) → spring
  2. Segment(C1, C2) → platform
  3. Segment(PS, PS + (0, 0.5)) → end
  4. Segment((time, 0), (time, f(time))) → ver
  5. Textfield(x0) → Inpx0
  6. Textfield(xprime0) → Inpxprime0
  7. Textfield(m) → Inpm
  8. Textfield(k) → Inpk
  9. Segment((0, f(time)), (time, f(time))) → hor
  10. Segment((x(A2), 0), (x(A2), 0) + (0, 0.5)) → endFixed
  11. CurveCartesian((2 * sin((((10 * 2) * π) * (t - 1 / 2) / (y_0 - 1 / 2)))) + x(A2), t, t, 1 / 2, y_0) → springFixed
  12. Ray((-5, 0), (-100, 0)) → eqpos

AI Drawing Prompt Reference

Draw a graph of an undamped spring's vibration. The spring is fixed on a platform with two endpoints. The spring starts vibrating from the center of the platform. The vibration trajectory is a sine curve. There are connecting lines between the platform and the spring, and the direction of vibration is perpendicular to the platform. The graph includes the spring, platform, endpoints, vibration direction, and connecting lines. The construction order is to draw the platform and endpoints first, then the spring, and finally add the vibration direction and connecting lines.
The prompt above was compiled from the original drawing commands and is for reference only.