# Circular Motion

Let's consider the following parametrized curve
- x(t) = cos(a*t)
- y(t) = sin(b*t)

These curves are called Lissajous curves after an 18th century
physicist. They occur in models of
oscillatory motion in two dimensions; for example, two
coupled spring-mass systems.

## Question #2

- In Maple, plot Lissajous curves by varying
*a* and *b*.
Sketch the curves in your lab report and indicate the direction
they were drawn.
- a := 1; b := -1;
- a := 3; b := 4;
- a := Pi; b := 4;

Hint: use the command

```
ParamPlot([cos(a*t), sin(b*t)], t = -Pi..Pi);
```

where you substitute in explicit values of *a* and *b*.
- How does the last curve differ from the earlier ones?
Use Maple commands like

`plot([cos(Pi*t), sin(t), t= 0 ..100]);`

to explore the long-term behavior of this curve. What
will the curve look like as *t* approaches infinity?

**Next: **It's Like Riding a Bicycle

**Up: **Introduction

**Previous: **Parametrizing Planar Curves

Robert E. Thurman<thurman@geom.umn.edu>
Jeremy Case
Document Created: Mon Feb 20

Last modified: Tue Feb 27 08:51:21 1996