How Does Charging a Ball Affect Its Pendulum Motion?

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When a positively charged ball is released from rest below a positively charged plate, it initially experiences a slight attraction due to its neutral state. However, once the ball is also positively charged, it encounters a repulsive force from the plate. This change in force dynamics raises the question of how it affects the pendulum's period. The discussion suggests that despite the repulsion, the fundamental characteristics of the pendulum's motion remain similar, implying that the period may not significantly change. Ultimately, the period of the pendulum motion is likely to stay the same, as the underlying equations governing its motion remain consistent.
einsteinette
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HI,

So say you have a small ball hanging vertically below a positively charged plate. When the ball is released from rest with the string at a small angle to the vertical, it swings in periodic pendulum motion. If the ball is now positively charged, does the period increase, decrease or stay the same? And why?

- Well at first, when it's neutral, there would be a slight attraction between the ball and the charged plate. But when the ball becomes positive as well, there would be now a slight repulsion. So would it stay the same?
 
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Do you know the differential equation for a simple pendulum? You could derive a similar equation with the electric force included. The solution should have the same form, so the period should be fairly obvious
 

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