f1 f1 f1 B ω2MHP/ ω0 ω2MLP /ω0 ωexact/ ω0 0.01 0.02 0.10 0.05 0.07 0.15 0.12 0.14 0.13 0.03 0.05 0.01 0.02 0.01 0.02 0.10 0.05 0.08 0.20 0.15 0.30 0.40 -0.05 -0.01 0.10 - -0.08 0.01 0.02 0.06 0.03 0.05 0.10 0.04 0.12 0.16 0.02 0.04 0.01 0.03 0.73513 0.76452 0.966336 0.823497 0.885144 1.07527 0.894785 0.949597 0.92592 0.825353 0.935453 0.761675 0.89998 1.01302 1.02191 1.03587 1.0494 1.06025 1.08029 1.17802 1.31772 1.43909 0.869297 0.844398 0.808686 0.68875 1.01302 1.02192 1.03603 1.04941 1.0603 1.0811 1.178 1.31768 1.43654 0.869339 0.844862 0.808704 0.702734 1.01302 1.02191 1.03584 1.0494 1.06025 1.08014 1.17802 1.31774 1.43667 0.869302 0.844401 0.808711 0.69135

Table 4: Comparison of the calculated values of ω2 /ω0in this paper for hexapole, octopole and decapole superpositions with the values obtained by modified Lindstedt- Poincare approximation [11] and the exact values.

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