Taming Chaos In An Array Of Pendulums

Woodrow Shew

A real coupled array of ten damped, driven, nonlinear pendulums was designed, built, and studied. When the pivot was driven in a circle of radius 3 cm at a frequency of 8.5 rad/sec, the homogenous array behaved chaotically. The pendulums were then randomly disordered so that their lengths fell in a range 12 to 20 cm. Then the same driving parameters forcing this heterogenous array produced periodic motion. Taming chaos with disorder in this parameter regime was determined to depend upon the arrangement of long and short pendulums in the disordered array and was independent of the initial conditions (initial positions and velocities between ±0.1 rad and ±0.1 rad/sec). The construction and use of the apparatus containing the array is described in detail.