Lissajous - oscillatory motion in two dimensions
Two masses on springs (harmonic oscillators) move at right angles to one another in a plane.
One mass moves on the X axis: .
The second mass moves on the Y axis:
You can vary all the parameters.
The point {x(t),y(t)} traces a curve on the plane.
Can you make the curve traced out be a circle? an ellipse? a straight line?
What determines the orientation of the ellipse? the straight line?
In general, can you tell how many loops the curve will have and which way they will be oriented?