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I did the system 1/2 mv^2=1/2kx^2+u m g x
for energy conservation

u m g=k x for spring remaining compressed at the maximum compressed position

fudge

So wait, is u your coefficient of static friction?

yeah

well I got du/dx=-(kx+umg)/(mgx)

which, as expected, gives me kx=umg hahaha

then I did the system;
1/2 mv^2=1/2kx^2+u m g x
kx=umg
and got u=(v sqrt(k))/(g sqrt(3m))

which... is wrong

oh wait that's stupid, that assumes u_s=u_k which is totally not true I'm stoopid

That should work

\[kx= u mg\]

Ah ok I see

figured it out now tho

thanks

Cool question though, thanks for sharing :)