<< Graphics`Pendulum`

Do[PlotPendulum["w", "th", 1.5, 0.5, 2/3, β, 0, 2, 1000, 
        100], {β, 0, 1, 0.01}]

periodic  =  {0.9, 0.5, 2/3, 0};

phase  =  {"w", "th"};

default  =  {0, 0};

PlotPendulum[phase, periodic, default, 1000, 100]