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Table 1 Comparison between the numerical frequency \(\omega\), the approximate frequency obtained by present method (given in Eq. 13) and other existing frequencies (Hamdan and Dado 1997; Wu et al. 2003) for \(\alpha = \beta = 1\) 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 1.34288 1.20953 1.24841 1.20953 1.32217 1.37581
9.93 7.04 9.93 1.54 2.45
10 1.38928 1.22074 1.26285 1.22074 1.35084 1.40388
12.13 9.10 12.13 2.77 1.05
15 1.40138 1.22295 1.26570 1.22295 1.35672 1.40955
12.73 9.68 12.73 3.19 0.58
20 1.40632 1.22373 1.26671 1.22373 1.35883 1.41158
12.98 9.92 12.98 3.38 0.38
25 1.40883 1.22409 1.26718 1.22409 1.35981 1.41252
13.11 10.05 13.11 3.48 0.26
30 1.41029 1.22429 1.26743 1.22429 1.36035 1.41304
13.19 10.13 13.19 3.54 0.20
50 1.41261 1.22458 1.26781 1.22458 1.36113 1.41379
13.31 10.25 13.31 3.65 0.08
100 1.41375 1.22470 1.26797 1.22470 1.36147 1.41411
13.37 10.31 13.37 3.70 0.03
200 1.41408 1.22473 1.26801 1.22473 1.36155 1.41419
13.39 10.33 13.39 3.72 0.00
500 1.41419 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 1.36157 1.41421
13.40 10.33 13.40 3.72 0.00
  1. The absolute relative error has been also computed