Symmetry behind charged spring-mass system in Electric field

In summary, the conversation discusses the rest and maximum positions of a mass-spring-electric field system, with x = EQ/k as the amplitude of the motion. The reason for the symmetry between the two positions is due to the equivalence of this problem to a vertical spring mass system with EQ replacing mg.
  • #1
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Homework Statement
Please see below
Relevant Equations
Please see below
For this problem,
1673242419091.png

If we assume that x = 0 is where the spring connects to the wall, then the rest position of the mass-spring-electric field position is x = EQ/k and the max position is x = 2EQ/k. Is there a reason for the symmetry between the rest position and max position? (The symmetry being: max position = rest position + EQ/k)

Many thanks!
 
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  • #2
The reason is that in this case EQ/k is the amplitude of the motion. Note that this problem is equivalent to a vertical spring mass system with EQ replacing mg.
 
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  • #3
kuruman said:
The reason is that in this case EQ/k is the amplitude of the motion. Note that this problem is equivalent to a vertical spring mass system with EQ replacing mg.
Thanks for your reply @kuruman! Whoops, forgot amplitude was max position - rest position, why was I thinking about symmetry??!
 

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