Proving SHM for charged spring mass system in electric field

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The discussion focuses on understanding the derivative of a constant in the context of a charged spring-mass system in an electric field. The user initially questions why a specific highlighted statement is true, particularly regarding the constant value x_0. They realize that the derivative of x_0 with respect to time is zero, indicating no change in the rest position over time. This rest position is defined by the balance of forces acting on the block. The user expresses gratitude for the clarification received.
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Homework Statement
Problem below.
Relevant Equations
Problem below.
For part (f)
1674159276690.png

Solution is
1674159332251.png


I don't understand why the bit highlighted in yellow is true.

Would anybody be kind enough to help.
 
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x_0 is a constant value. What is the derivative of constants?
 
nasu said:
x_0 is a constant value. What is the derivative of constants?
I see now. ## \frac {dx_0} {dt} = 0 ## as for each differential time, there is no change in the rest position. This is because rest position is function of where the forces acting on the block are equal only. Right?

Thank you for the help @nasu .
 

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