Adamped driven pendulum may be modeled using the nonautonomous system of differential equations defined by

(8.12)

d2θ

dt2 + k dθ

dt +

g l

sin(θ) = Ŵ cos(ωt ), where k is a measure of the frictional force, Ŵ and ω are the amplitude and frequency of the driving force, g is the acceleration due to gravity, and l is the length of the pendulum. Plot a Poincaré map for this system when k = 0.3, Ŵ = 4.5, ω = 0.6, and g l = 4.