[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]The load on an ideal zip line (that is, without friction) behaves similarly to that of a double pendulum. The difference lies in the fact that now the pulley (the first pendulum) does not trace a circular arc, but rather an elliptical arc, as its path is determined by the length of the cable, which is the sum of the distances from the pulley to the ends A and B.[br][br]We have utilized the slider script to record the maximum speed reached (with or without load). Thus, we can observe that the load (red point) can move faster than the pulley connected to the cable (blue point). In reality, the load is usually very close to the pulley, which minimizes, along with friction, the oscillations caused by the load.

[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][color=#cc0000][br][br]# Move M1 and M2 and record the maximum speed[/color][color=#999999][br][color=#999999]SetValue[/color](v1, vt1 + dt gt1)[/color][color=#999999][br][color=#999999]SetValue[/color](v2, vt2 + dt gt2)[/color][color=#999999][br][color=#999999]SetValue[/color](M1, M1 + dt v1)[/color][color=#999999][br][color=#999999]SetValue[/color](M2, M2 + dt v2)[/color][br][color=#0000FF]SetValue(vMax1, Max(abs(v1), vMax1))[/color][br][color=#0000FF][color=#0000FF]SetValue[/color](vMax2, [color=#0000FF]Max[/color](abs(v1 + v2), vMax2))[br][/color][color=#cc0000][br]# Add the positions of M1 and M2 to the record for the polylines traces[/color][color=#0000FF][br][color=#0000FF]SetValue[/color](reg1, Append(reg1, M1))[br][color=#0000FF]SetValue[/color](reg2, [color=#0000FF]Append[/color](reg2, M2))[/color][br][br][br][br][br][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][br]