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LissaLab Carbon for iPad


This little app, with a superb oscilloscope look-and-feel, lets you experiment with different forms of Lissajous figures. The app’s interface closely simulates oscilloscope behavior giving you a full control of the input signal as well as the possibility to change typical display parameters like the trace focus and intensity. 

Since the oscilloscope display operates in X-Y mode (plotting one channel against another) input signal properties must be adjustable for each channel separately. 

According to the definition of Lissajous curves the input signals for both channels are described by a system of parametric equations: 

which can be also put in the following way:


A – amplitude, ƒ –frequency and φ - phase shift. 

Each of the mentioned above parameters can be changed manually using dedicated dial knobs. This gives you a great possibility to explore all variations of the Lissajous figure patterns. 
See some screenshots, if you are interested.


Now LissaLab also plays sine waves separately for each channel with a frequency multiplied by 10 in a range from 40 to 1000Hz. This is due to the fact that base frequency 0-100Hz can be hardy heard (not to mention that sound in frequency lower than 20Hz is an infrasound which we won't normally hear).


Launch the application and at first try to play with frequency knob for both channels X and Y. Oscilloscope display responds immediately. Once the graph gets stable start turning amplitude or/and phase shift knob. See how the graph get changed. 

Hint #1: Typical (book) figure patterns can be easily obtained by setting frequency precision to 10 Hz. 

Hint #2: The more granular input frequency the more unstable graph. If you change the frequency of a stable graph just a little (e.g. ƒx = 50.0 Hz → 50.1 Hz and ƒy = 30.0 Hz → 29.9 Hz) then we get a kind of moving, rotating original graph. 

Hint #3: If you set the same frequency for both channels (e.g. ƒx = 50 Hz & ƒy = 50 Hz) and then you play with channel Y's phase shift simultaneously keeping still φx = 0, then the displayed figure will start changing from a straight line to an oval. Why is that? Curious? Check then this link with further readings

Have fun and feel like a lab staff member!