Proving SHM for charged spring mass system in electric field

[Nway]

Homework Statement

Problem below.

Relevant Equations

Problem below.

For part (f)

Solution is

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

Would anybody be kind enough to help.

 

[nasu]

x_0 is a constant value. What is the derivative of constants?

 

[Nway]

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 .