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Damping refers to limiting movement of something. In England, a 'Shock absorber' is called a 'Damper,' because that's what a shock absorber does - it limits the movement of some oscillating mass (like your car body) so that it doesn't shake out of control.

Any analog electric meter has some dampening mechanism in it so that quickly changing readings won't shake the movement too much. This makes for more accurate average readings of a quantity. If you need to see the changes that are occuring rapidly, like transient voltages or pulses, you wouldn't use an analog meter, you would use an oscilloscope

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