f1 B ω2MHP/ ω0 ω2MLP /ω0 ωexact/ ω0 0.01 0.05 0.10 0.11   0.12 0.13 0.14 0.15 0.155 0.1565 0.722439 0.792221 0.913755 0.947125 0.986189 1.03385 1.09633 1.19283 1.28435 1.3404 0.999569 0.987927 0.939194 0.921209 0.898183 0.867497 0.8232207 0.744627 0.649963 0.556534 0.999568 0.987913 0.939082 0.921043 0.897928 0.867083 0.822454 0.742729 0.644365 0.527906 0.999569 0.987926 0.939193 0.921214 0.898204 0.867561 0.823418 0.745686 0.655595 0.582921

Table 1: Comparison of the calculated values of ω2 /ω0 in this paper for only hexapole superposition with the values obtained by modified Lindstedt-Poincare approximation [11] and the exact values.

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