# Exploring the Relationship Between Energy and Motion

## What variables were plotted in the mathematical model development lab?

Independent Variable: height (displacement of the mass)

Dependent Variable: velocity (speed) of the mass

Dependent Variable: tension in the string

## Answer:

In the lab, the independent variable (x-axis) that was plotted is the height (displacement of the mass), and the dependent variable (y-axis) options are the velocity (speed) of the mass and the tension in the string.

When developing a mathematical model in the lab, it is crucial to plot the variables to analyze their relationship. In this case, the model connects the stored energy in the mass at maximum height to the total gain in kinetic energy of the mass as it passes through the equilibrium.

The independent variable, which is plotted on the x-axis, is the height or displacement of the mass. This means that the height is manipulated in the experiment to observe its impact on the other variables.

The dependent variable, which is plotted on the y-axis, can be either the velocity (speed) of the mass or the tension in the string. These variables react to changes in the independent variable and can be measured or observed during the experiment.

By plotting the height on the x-axis and either the velocity or tension on the y-axis, we can visually represent the relationship between these variables and analyze the data collected from the experiment.

Exploring mathematical models like this helps us understand the underlying principles of energy and motion, leading to exciting discoveries and advancements in various fields.