Driven Damped Pendulum
dω/dt = -βω - α sin(ϑ) + A sin(ϑ) sin(2πt)
dϑ/dt = ω

Driving amp A:   Friction β:   α:
Ntransient: Nplot:
A graph of ϑ(t) versus t
A graph of ω versus ϑ
A graph of ω(t=i) versus ϑ(t=i)
There are many different paths in parameter space to chaos. Some undergo period doubling.