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1. This is due to static charges on the body. These charges are produced by friction between the clothes and skin.
2. The black plug conects your body to earth. The static charges are reduced, hence a decrease of voltage.
3. Touching the case has the same effect as earthing. This reduces the static chrages and decrease the voltage.
4. The ac mains socket carries electric current. There are time varying (50 Hz) electric and magnetic fields at the vicinity of the socket. This causes electromagnetic induction, which will be picked up by the CRO.
5. These are so called "Llissajous figures". They are produced by inputting sinusoidal waves (signals) into the X and Y inputs of the CRO. For given X and Y voltages input, with a given freuqncies (the frequency for X and Y may or may not be the same) and phase difference, a certain firgure is traced out and displayed on the CRO screen. By varying all or any of the voltages, frequencies, or the phase differences, a variety of figures are obtained.
For example, the simplest figure is a "striaght line", which is produced if both X and Y signals are of the same voltage, same frequency and in pahse (zero phase difference).
If the X and Y signals are of the same voltages and frequency, but are 90 degrees out of phase, a circle is obtained. For different X and Y voltages, an ellipse is produced.