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Superposition of Transverse Simple Harmonic Waves

​
horizontal
frequency
1
amplitude
1
phase
0
vertical
frequency
1
amplitude
1
phase
0
run
This Demonstration shows the motion resulting from the superposition of two simple harmonic oscillations in perpendicular directions:
x=
A
x
cos(
ω
x
t+
φ
x
)
y=
A
y
cos(
ω
y
t+
φ
y
)

Details

Two interesting possibilities are superposition of two simple harmonic motions: the same frequency but varying phase difference; simple harmonic waves with different frequencies, producing Lissajous figures.

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