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We applied multiple parameters method
(MPM) to obtain natural frequency of the nonlinear oscillator with rational
restoring force. A frequency analysis is carried out and the relationship
between the angular frequency and the initial amplitude is obtained in
analytical/numerical form. This equation is analyzed in three cases: the
relativistic harmonic oscillator, a mass attached of a stretched elastic wire
and oscillations of a punctual charge in the electric field of charged ring.
The three and four parameters solutions are obtained. The results obtained are
compared with the numerical solution, showing good agreement.