Lissajous - oscillatory motion in two dimensions

Two masses on springs (harmonic oscillators) move at right angles to one another in a plane.[br][br]One mass moves on the X axis: [math]x(t) = Ax Sin(ω_xt)[/math]. [br]The second mass moves on the Y axis: [math]y(t) = Ay Sin(ω_yt + ϕ)[/math][br][br]You can vary all the parameters.[br][br]The point {x(t),y(t)} traces a curve on the plane.[br][br]Can you make the curve traced out be a circle? an ellipse? a straight line?[br]What determines the orientation of the ellipse? the straight line?[br][br]In general, can you tell how many loops the curve will have and which way they will be oriented?[br]

Information: Lissajous - oscillatory motion in two dimensions