Abstract
In the previous paper, the general theory of exact solutions in a family of Duffing oscillators including hard, soft and snap-through spring systems was studied. In particular the paper discussed the hard spring system in detail, and a listing of the numeration program was included. As a continued report, the soft spring system is dealt with here in detail. All the free vibrations in a family of Duffing oscillators are solved exactly and formally in terms of a family of Jacobian elliptic functions ; however, their precise numeration is a very important task. The present study is devoted to discussing excellent algorithms/programs. A FORTRAN program with the precision of REAL * 16 is presented, which ensures an accuracy with relative error of less than 10-30. The listing of the program and numerical results of the dynamics of the Duffing oscillator with the soft spring system are demonstrated.
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