Find when spring oscillates less than X

[Acreol]

Given the spring equations in the desmos (pretty sure they are standard from
https://en.wikipedia.org/wiki/Harmonic_oscillator
, but if they aren't please say so), how would you find when the spring will oscillate with a rate of change less than X (I'm using this to determine when the spring is steady)

https://www.desmos.com/calculator/63lncxcjmk

Also I'm not really sure what level of physics this is so if I got it wrong, please let me know ;P

 

[sophiecentaur]

with a rate of change less than X

I'm not sure what you mean by "X". Where does this fit into the standard equations? If the damping is linear then the motion has exponential decay and the decay graph has the same (scaled) shape for all start amplitudes. Envelope of Amplitude / Rate of change / higher derivatives etc. will all have the exponential form so it looks as if the answer to your question could be "it's easy" Just solve the equation for rate of change = X.