Recently, I found that Google Copilot can solve a nonlinear but solvable equation like coulomb damping[1], just by searching for "r''(t)=-r(t)-sgn(r'(t))/10, r(0)=0, r'(0)=1" [2], whether Copilot's time-dependent answer is correct or not aside.
Is it possible to refine the following command
DSolve[{r''[t] == -r[t] - Sign[r'[t]]/10, r[0] == 0, r'[0] == 1}, r[t], t]
to obtain the same analytic result in Mathematica v.14.0 ?
[1] https://en.wikipedia.org/wiki/Coulomb\_damping
[2] https://www.google.com/search?q=r%27%27%28t%29%3D+-r%28t%29+-sgn%28r%27%28t%29%29%2F10%2C+r%280%29%3D0%2C+r%27%280%29%3D1
