Pendulum isn't a simple harmonic system

Ideas
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1

Pendulum isn’t a simple harmonic system, its period (the time for one complete cycle) rely on the amplitude of the swing. Theoretical computations show the period approaches infinity as the amplitude of the swing approaches Pi… that’s cool physics!

Illustrating this fact using Wolfram Language was so easy!

export.gif

Manipulate[
 Show[Graphics[Dynamic@{
     {Dashed, Circle[{0, 0}, 2.5]},
     {RGBColor[0.24, 0.6, 1.], Thick, 
      Line[{{0, 0}, 2.5 {Sin[odeSolve[run]], -Cos[odeSolve[run]]}}]},
     {Black, PointSize[.015], Point[{0, 0}]},
     {Black, PointSize[.015], 
      Point[2.5 {Sin[odeSolve[run]], -Cos[odeSolve[run]]}]},
     {EdgeForm[{Blue, Thick}], RGBColor[0.24, 0.6, 1.], 
      Disk[2.5 {Sin[odeSolve[run]], -Cos[odeSolve[run]]}, 0.2]}
     }]
  , PlotRange -> {{-3, 3}, {3, -3}}, ImageSize -> Medium, 
  Background -> Lighter[Gray, 0.5], Axes -> True, 
  AxesOrigin -> {-3, -3},
  PlotLabel -> Style["modelo no linealizado", Black, Bold]],
 {{run, 0, Style["time", 12]}, 0, 20, ControlType -> Animator, 
  AnimationRunning -> False, AnimationRate -> 1, 
  Appearance -> "Labeled", ImageSize -> Medium, 
  AppearanceElements -> {"PlayPauseButton", "ProgressSlider", 
    "ResetButton", "StepLeftButton", "StepRightButton"}},
 Initialization :> (odeSolve[
     t_] := (\[Theta][t] /. 
      First[NDSolve[{\[Theta]''[tt] + 9.8/2.5 Sin[\[Theta][tt]] == 
          0, \[Theta]'[0] == 
          0, \[Theta][0] == .99 \[Pi]}, \[Theta], {tt, 0, 30}]])), 
 Alignment -> Center
 ]