Lissajous figures
This simulation shows the superposition of two perpendicular harmonic
oscillations. We have
x = A1 cos(ω1
t)
in the horizontal direction and
y = A2
cos(ω2 t + φ)
in the vertical.
Above
one can see the evolution of the phasor for the horizontal oscillation and
on the left the one for the vertical motion.
-
You can choose in the left panel the amplitudes A1 = A1
and A2 = A2, the frequencies ω1 = ω1
and ω2 = ω2 and the relative phase φ
(in degrees), as well as the interval Δt between points
and their number.
-
To erase the figure, click it with the mouse.
Activities
Enter the following values and discuss the corresponding evolution
|
A1
|
A2
|
ω1
|
ω2
|
φ
|
|
1
|
1
|
1
|
1
|
0
|
|
1
|
1
|
1
|
1
|
45
|
|
1.5
|
1
|
1
|
1
|
0
|
|
1.5
|
1
|
1
|
1
|
45
|
|
1
|
1
|
1
|
1
|
0
|
|
1
|
1
|
2
|
1
|
45
|
|
1
|
1
|
2
|
1
|
0
|
|
1
|
1
|
3
|
2
|
0
|
|
1
|
1
|
3
|
2
|
45
|
|
1
|
1
|
5
|
7
|
0 (with Δt = 0.01)
|
|
1
|
1
|
5
|
7
|
45 (with Δt = 0.01)
|
|
1
|
1
|
1.35719
|
2
|
45
|
-
In which cases is periodic the orbit?
-
When the orbit is periodic, what determines the number of maxima (and
minima) in each direction?
This is an English translation of the Basque original for a course
on mechanics, oscillations and waves.
It requires Java
1.5 or newer and was created by Juan
M. Aguirregabiria with Easy
Java Simulations (Ejs) by Francisco
Esquembre. I thank Wolfgang Christian and Francisco Esquembre for
their help.