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Table 2 Comparison between the numerical frequency \(\omega\), the approximate frequency obtained by present method (given in Eq. 13) and other existing frequency (Hamdan and Dado 1997; Wu et al. 2003) for \(\alpha = \beta = 2\) as well as several large amplitudes

From: An analytical coupled technique for solving nonlinear large-amplitude oscillation of a conservative system with inertia and static non-linearity

A Numerical frequency \(\omega_{e}\) Hamdan and Dado (1997) (error%) Wu et al. (2003) (error%) Present method (error%) \(\omega_{0}\)
\(\omega_{0}\) \(\omega_{1}\) \(\omega_{0}\) \(\omega_{1}\)
5 1.37132 1.21687 1.25786 1.21687 1.34073 1.39406
11.26 8.27 11.26 2.23 1.66
10 1.40006 1.22272 1.26541 1.22272 1.35613 1.40898
12.67 9.61 12.67 3.14 0.64
15 1.40707 1.22384 1.26685 1.22384 1.35913 1.41187
13.02 9.96 13.02 3.41 0.34
20 1.40986 1.22424 1.26736 1.22424 1.36020 1.41289
13.17 10.11 13.17 3.52 0.22
25 1.41127 1.22442 1.26760 1.22442 1.36069 1.41337
13.24 10.18 13.24 3.59 0.15
30 1.41207 1.22452 1.26773 1.22452 1.36096 1.41363
13.28 10.22 13.28 3.62 0.11
50 1.41335 1.22466 1.26791 1.22466 1.36135 1.41400
13.35 10.29 13.35 3.68 0.05
100 1.41397 1.22472 1.26799 1.22472 1.36152 1.41416
13.39 10.32 13.39 3.71 0.01
200 1.41414 1.22474 1.26801 1.22474 1.36156 1.41420
13.40 10.33 13.40 3.72 0.00
500 1.41420 1.22474 1.26802 1.22474 1.36157 1.41421
13.40 10.33 13.40 3.72 0.00
1000 1.41421 1.22474 1.26802 1.22474 1.36158 1.41421
13.40 10.34 13.40 3.72 0.00
  1. The absolute relative error has been also computed