When a pan of cold water is placed on a hot flat electric stovetop, the immediate vibration or movement of the pan is likely due to a phenomenon called "thermal shock." Here's how it happens:
Temperature difference: The cold water in the pan has a significantly lower temperature than the hot electric stovetop. When the cold pan comes into contact with the hot surface, there is a sudden and extreme temperature difference between the two.
Expansion and contraction: The rapid change in temperature causes the materials (metal of the pan and the glass surface of the stovetop) to expand or contract at different rates. The metal of the pan and the glass surface of the stovetop have different coefficients of thermal expansion, meaning they expand or contract by varying amounts when exposed to temperature changes.
Uneven expansion: Due to the uneven expansion or contraction of the pan and the stovetop, areas of the pan and the glass surface might have slight variations in height or curvature. This unevenness can cause the pan to lose stability and start to vibrate.
Vibrations: The vibrations occur as the pan tries to find a stable position on the hot stovetop. It might slightly lift on one side and then settle back, repeating the process rapidly. This creates the vibrating effect that you observe.
As the pan continues to heat up and reaches a more uniform temperature with the stovetop, the vibrations will likely diminish and eventually stop. Additionally, using a pan with a flat and even base, and allowing the pan to warm up gradually by starting with a lower heat setting, can minimize the intensity of the thermal shock and reduce the vibrations.