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  • $\begingroup$ yes,the real period is not 23.14,it doesn't matter this question,and NIntegrate::slwcon: Numerical integration converging too slowly; suspect one of the following: singularity, value of the integration is 0, highly oscillatory integrand, or WorkingPrecision too small. >> still exist,it means the result is not accurate or it only means the Convergence is slow ? $\endgroup$ Commented Nov 6, 2019 at 9:18
  • $\begingroup$ and if the real solution of p1 is continous,will the figure of p1 is continous means the solution of p1 is continus? why when i export p1 data to EXCEL and plot in EXCEL,the figure is discontinous? $\endgroup$ Commented Nov 6, 2019 at 9:21
  • $\begingroup$ NIntegrate::slwcon is a warning, not an error. If you get an answer without NIntegrate::ncvb it should be good. Sorry, I have no idea about your plot in Excel. $\endgroup$ Commented Nov 6, 2019 at 9:30
  • $\begingroup$ you have solved my question and thanks a lot! $\endgroup$ Commented Nov 6, 2019 at 10:19
  • $\begingroup$ @dcydhb I believe p1 is discontinuous when x'[t] == 0. Plot cannot figure that out on its own. Compare with Plot[p1, {t, 40, 44}, PlotRange -> All, Exclusions -> (x'[t] == 0 /. First@s1)]. $\endgroup$ Commented Nov 6, 2019 at 12:50