"either the pendulum or counterweight eventually collides with its pulley), except for formula_3.However, the swinging Atwood's machine with formula_4 has a large parameter space of conditions that lead to a variety of motions that can be classified as terminating or non-terminating, periodic, quasiperiodic or chaotic, bounded or unbounded, singular or non-singular due to the pendulum's reactive centrifugal force counteracting the counterweight's weight.