Let's consider the following parametrized curve
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.
- x(t) = cos(a*t)
- y(t) = sin(b*t)
- In Maple, plot Lissajous curves by varying a and b.
Sketch the curves in your lab report and indicate the direction
they were drawn.
Hint: use the command
- a := 1; b := -1;
- a := 3; b := 4;
- a := Pi; b := 4;
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
Previous: Parametrizing Planar Curves
Robert E. Thurman<email@example.com>
Document Created: Mon Feb 20
Last modified: Tue Feb 27 08:51:21 1996