Simple Harmonic Motion Energy Problem

[SirPlus]

Homework Statement

Derive the equilibrium state of a simple harmonic oscillation and show that the derivative of the maximum displacement is s^{'} = 2 \sqrt{E}

Homework Equations

F = -k x

The Attempt at a Solution

m a = -k s
\rightarrow ms^{''} = -k s
\rightarrow s^{''} = -ω s

Homework Statement

I don't know how to obtain the second part of the question, I've tried so many ways and all have failed, PLEASE HELP *IMPORTANT

 

[voko]

The derivative of the maximum displacement with respect to what?

 

[SirPlus]

With respect to time...

 

[voko]

The maximum displacement does not depend on time, it is a constant.