Vernier Software and Technology
Vernier Software & Technology

Crawling Around: Parametric Plots

Figure from experiment 23 from Real-World Math Made Easy

Introduction

Imagine you are observing a bug crawling around in a figure eight path on the floor. If we define a Cartesian x, y plane on the floor, and you wished to completely describe the bug’s movements graphically, you would need to create a graph in three dimensions. This graph would need one axis to describe the x movement of the bug, another axis for its y movement, and a third axis for the time elapsed during the motion.

It is difficult to portray a graph in three dimensions on two-dimensional paper. It is relatively simple, however, to create a two-dimensional graph.

In this activity, you will model the bug’s movement by breaking the motion down into its x and y components. You can then use parametric equations to separately describe each of these components as a function of time. Finally, you will use the parametric mode in your calculator to combine these graphs and create a model that describes the motion of the bug.

Objectives

  • Record the x- and y-coordinates of a rod moving in a figure-eight pattern.
  • Use the recorded motion information to separately model the x- and y- motion as a function of time.
  • Plot the experimental data in a y versus x graph.
  • Plot the x- and y-models parametrically for comparison to the experimental data.

Sensors and Equipment

This experiment features the following Vernier sensors and equipment.

Option 1

Option 2

Additional Requirements

You may also need an interface and software for data collection. What do I need for data collection?

Standards Correlations

See all standards correlations for Real-World Math Made Easy »

Real-World Math Made Easy

See other experiments from the lab book.

1Walk the Line - Straight Line Distance Graphs
2Making Cents of Math: Linear Relationship between Weight and Quantity
3Pool Plunge - Linear Relationship between Water Depth and Pressure
4Funnel Volumes - Volume and Weight
5Keep It Bottled Up - Rates of Pressure Increase
6Graph It in Pieces: Piecewise Defined Functions
7Mix It Up - Mixing Liquids of Different Temperatures
8Spring Thing - Newton's Second Law
9Stretch It to the Limit - The Linear Force Relation for a Rubber Band
10What Goes Up - Position and Time for a Cart on a Ramp
11That's the Way the Ball Bounces - Height and Time for a Bouncing Ball
12Walk This Way - Definition of Rate
13Velocity Test - Interpreting Graphs
14From Here to There - Applications of the Distance Formula
15Under Pressure - The Inverse Relationship between Pressure and Volume
16Light at A Distance - Distance and Intensity
17Chill Out: How Hot Objects Cool
18Charging Up, Charging Down - Charging a Capacitor
19Bounce Back - The Pattern of Rebound Heights
20Sour Chemistry - The Exponential pH Change
21Stepping to the Greatest Integer: The Greatest Integer Function
22Swinging Ellipses - Plotting an Ellipse
23Crawling Around: Parametric Plots
24Lights Out! - Periodic Phenomena
25Tic, Toc: Pendulum Motion
26Stay Tuned: Sound Waveform Models
27Up And Down: Damped Harmonic Motion
28How Tall? Describing Data with Statistical Plots
29And Now, the Weather - Describing Data with Statistics
30Meet You at the Intersection: Solving a System of Linear Equations
31Titration Curves: An Application of the Logistic Function

Experiment 23 from Real-World Math Made Easy Lab Book

<i>Real-World Math Made Easy</i> book cover

Included in the Lab Book

Vernier lab books include word-processing files of the student instructions, essential teacher information, suggested answers, sample data and graphs, and more.

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