¡TUTORIAL! Simulador en Geogebra - Péndulo simple

Building a Simple Pendulum Simulator

Initial Setup and Variables

• The simulator will be built step by step, starting with the identification of key variables for the pendulum simulation.

• The angle of the pendulum is limited to 90 degrees with an increment of 1 degree for adjustments.

Defining Key Parameters

• Variables related to gravity and length are established: gravity ranges from 0 to 100, while length varies from 0 to a maximum of 20 meters. These will be user-defined inputs.

• Input boxes will allow users to enter values for the pendulum's length in meters and gravity (standardized at approximately 9.81 m/s²).

Understanding Pendulum Dynamics

• The movement of a simple pendulum is independent of the mass attached; this principle is crucial for understanding its dynamics.

• The formula for calculating the period of a simple pendulum is introduced: T = 2pi sqrtL/g , where L is length and g is gravity. This allows dynamic changes based on user input.

Angular Position Calculation

• An angular position variable, denoted as alpha, depends on initial angle and time, calculated using alpha(t) = x_0 cdot sqrtg/L t . A slider will control time increments from 0 to 100 times the period with an increment of 0.01 seconds.

• The mathematical foundation includes solving differential equations relevant to pendulum motion, which may be explored in future demonstrations or videos.

Visual Representation and Controls

• A graphical representation involves creating points and segments that visually depict the pendulum's motion around a fixed point (point A). This segment represents the string or rod of the pendulum moving vertically based on angular displacement (alpha).

• Animation speed can be adjusted through controls; buttons are created for play, pause, and reset functionalities that manage simulation states effectively. For instance, setting a boolean value starts or pauses movement accordingly.

Final Adjustments and Features

• A dynamic text feature displays elapsed time during simulation akin to a stopwatch, enhancing user interaction by tracking motion duration accurately. Additionally, reference lines are added for visual clarity regarding axis alignment during simulations.

Creating a Simple Pendulum Simulator in GeoGebra

Overview of the Simulation Process

• The simulation will focus on creating a graph for simple harmonic motion generated by the pendulum's movement, specifically using a lentil at the extreme of Mendel.

• The next step involves setting up the graphical view to visualize this motion effectively.

Setting Up Variables and Calculations

• Two auxiliary variables are introduced: x2 representing time and another variable related to the amplitude of the pendulum, which changes based on its angular position.

• To calculate bursts (the length corresponding to two times), a trigonometric function is used involving sine and angular position, establishing foundational calculations for the simulator.

Graphical Representation

• A point called "point" is created with complex coordinates to visualize in graphic view 2. Adjustments are made through properties settings to ensure proper display.

• The axes are adjusted for clarity; specifically, the x-axis represents time starting from zero, while ensuring it reflects the pendulum's amplitude accurately.

Final Adjustments and Functionality

• Further refinements include adjusting initial positions based on angle values and ensuring that both ends of the graph do not appear too cramped.

• The final output shows that as parameters like length change, both axes adjust automatically, demonstrating dynamic behavior in response to user input.

Conclusion and User Instructions

• A brief description concludes how to use the simulator effectively, including sliders for initial angles and input boxes for pendulum length and gravity settings.