t0 = 0; \[CurlyPhi]0 = 0.25; g = 9.81; l = 1.45; \[CurlyPhi]10 = 0; stepsize = 0.01; \[CurlyPhi]2[\[CurlyPhi]_] := (3*Sin[\[CurlyPhi]]*g)/(2*l) euler := Module[{ans, t, \[CurlyPhi], \[CurlyPhi]1}, ans = {{t0, \[CurlyPhi]0}}; \[CurlyPhi] = \[CurlyPhi]0; t = t0; \[CurlyPhi]1 = \[CurlyPhi]10; While[\[CurlyPhi] < 1.5708, \[CurlyPhi]1 = \[CurlyPhi]1 + stepsize*\[CurlyPhi]2[\[CurlyPhi]]; \[CurlyPhi] = \[CurlyPhi] + stepsize*\[CurlyPhi]1; t = t + stepsize; ans = Append[ans, {t, \[CurlyPhi]}] ]; ans] eulerans1 = Drop[euler, -1]; Last[eulerans1] grapheuler1 = ListPlot[eulerans1, AxesLabel -> {"t", "\[CurlyPhi]"}, PlotStyle -> {PointSize[0.01]}, GridLines -> Automatic] h = 0.0001; times = Module[{\[CurlyPhi]0, bns}, bns = {{0.2, 0.8819999999999192}}; \[CurlyPhi]0 = 0.22; While[\[CurlyPhi]0 < 1.32, bns = Append[ bns, {\[CurlyPhi]0, Last[Drop[Module[ {ans, t, \[CurlyPhi], \[CurlyPhi]1}, ans = {t0}; \[CurlyPhi] = \[CurlyPhi]0; t = t0; \[CurlyPhi]1 = \[CurlyPhi]10; While[ \[CurlyPhi] < 1.5708, \[CurlyPhi]1 = \[CurlyPhi]1 + h*\[CurlyPhi]2[\[CurlyPhi]]; \[CurlyPhi] = \[CurlyPhi] + h*\[CurlyPhi]1; t = t + h; ans = Append[ans, t] ]; ans], -1]]} ]; \[CurlyPhi]0 = \[CurlyPhi]0 + 0.02]; bns]; ListPlot[times, AxesLabel -> {"\[CurlyPhi]0", "T"}, PlotStyle -> {PointSize[0.01]}, GridLines -> Automatic] acceleration = 1.45*\[CurlyPhi]2[1.5708]