Free Damped Vibration
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This example demonstrates the motion of free damped vibration. Key mathematical concepts include differential equations and complex numbers. Using GeoGebra commands such as Line, ComplexRoot, and SolveODE, the example dynamically shows the decay process of vibration under different parameters. Suitable for high school physics and mathematics courses.
GeoGebra Commands & Parameters
Line(A, A + (1, initialY')) → eComplexRoot(charPoly) → z, wIf(y(z) ≟ 0, "" + (x(z)), "" + z) → zTextIf(y(w) ≟ 0, "" + (x(w)), "" + w) → wTextSolveODE((2 * p), w2, 0, initialX, initialY, initialY', endX, step) → DEIf(dampTest < 0, "Underdamped", If[dampTest > 0, "Overdamped", "Critically Damped"]) → text5
AI Drawing Prompt Reference
Demonstrate the motion of free damped vibration, showing the decay process under different parameters. Key elements include the vibration trajectory, marked complex roots, and text labels indicating vibration types. Start by drawing the vibration path, then mark the positions of the complex roots, and finally add text labels based on parameter conditions to classify vibration types, dynamically illustrating the decay process.
The prompt above was compiled from the original drawing commands and is for reference only.