[color=#0000ff][i][color=#0000ff][i][color=#999999]This activity belongs to the GeoGebra book [url=https://www.geogebra.org/m/mes4bgft]The Domain of the Time[/url].[/color][/i][/color][/i][/color][br][br]If we place a pendulum at the moving end of another, we obtain a [i]double pendulum[/i]. Although each of them continues to be governed by the stable period of an ordered motion, their combined movement results in chaos.[br][br]We can take advantage of the polyline generated by the trace to estimate the distance traveled by the second pendulum.

[b]SCRIPT FOR SLIDER anima[/b][br][br][color=#cc0000][color=#cc0000]# Calculate the elapsed seconds dt; add one second if t1(1) < tt[/color][/color][br][color=#999999]SetValue(tt, t1(1))[br]SetValue(t1, First(GetTime(), 3))[br]SetValue(dt, (t1(1) < tt) + (t1(1) − tt)/1000)[/color][br] [br][color=#cc0000]# Move M1 and M2[/color][color=#0000FF][br]SetValue(v1, vt1 + dt gt1)[br][color=#0000FF]SetValue[/color](v2, vt2 + dt gt2)[br][color=#0000FF]SetValue[/color](M1, M1 + dt v1)[br][color=#0000FF]SetValue[/color](M2, M2 + dt v2)[br][br][/color][color=#cc0000]# Add the position M2 to the record for the polyline trace[/color][color=#0000FF][br][color=#0000FF]SetValue[/color](reg, Append(reg, M2))[/color] [br][br][br][br][br][color=#0000ff][color=#999999][color=#999999][color=#0000ff][color=#0000ff][color=#999999][color=#999999]Author of the activity and GeoGebra construction: [/color][/color][/color][color=#0000ff][color=#999999][color=#999999][url=https://www.geogebra.org/u/rafael]Rafael Losada[/url].[/color][/color][/color][/color][/color][/color][/color]