An accurate relationship between frequency and amplitude to nonlinear oscillations

Figures & data

Table 1. Comparison of approximate frequencies with exact ones for the fourth-order approximation.

$\epsilon$	$A$	$a_3$	$a_5$	$a_7$	${\omega }_{\mathrm{WGEM}}$	$\left|\text{R.E}.\right|\mathrm{\%}$	${\omega }_{\mathrm{exact}}$
0.5	1	0.011390151796	0.0001297697	0.000001479	1.170781471	$4.47\times {10}^{-7}$	1.17078146596
1	1	0.0179606824	0.00032279884	0.0000058062	1.31777612231	$4.35\times {10}^{-6}$	1.3177760649655
5	1	0.03355928503	0.0011288575	0.00003800188	2.1504184036	0.000103890	2.1504161695
10	1	0.037701477675	0.0014256098	0.00005394209	2.86664558385	0.000190021	2.866640136632
1	10	0.424452613569	0.01808390269	0.0007708154	8.5336164063	0.000354099	8.533586188999
10	10	0.4298836965	0.018551477	0.000800920	26.81084000637	0.0003787595	26.81073845817
50	10	0.4303734199	0.01859393559	0.0008036728	59.91596743096	0.000381052	59.915739120788
5	100	4.30483766669	0.1860350925	0.0080429396	189.44608782375	0.000381570	189.4453649565
10	1000	43.049596970	1.860456814	0.080436267	2679.133430887	0.0003816276	2679.123206613