Abstract
A revised report and detailed summary of the previous papers are presented, in which exact solutions of the free oscillation in a system with a Duffing spring and a single degree of freedom are dealt with. It is well known that a theoretically exact solution to the homogeneous Duffing equation family (hard, soft and snap-through springs) is solved in terms of the Jacobian elliptic function family (sn u, cn u and dn u). However, their precise numeration is rather difficult using the constant-digit (regular) computer. An excellent algorithm and program are essential for avoiding such unfortunate cases in which almost all digits of the computed results are of poor accuracy for some complicated problems. A comprehensive discussion for relevant algorithms, and the listing of a final program for the hard spring system, are shown. Numerical results of the dynamics of a free oscillator with the hard spring are also discussed and demonstrated.
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