An enhanced analytical technique for nonlinear oscillators having a
harmonic restoring force is proposed. The approach is passed on the
change of the auxiliary operator by another suitable one leads to obtain
a periodic solution. The fundamental idea of the new approach is based
on obtaining an alternative equation free of the harmonic restoring
forces. This method is a modification of the homotopy perturbation
method. The approach allows not only an actual periodic solution, but
also the frequency of the problem as a function of the amplitude of
oscillation. Three nonlinear oscillators including restoring force, the
simple pendulum motion, the cubic Duffing oscillator, the Sine-Gordon
equation are offered to clarify the effectiveness and usefulness of the
proposed technique. This approach allows an effective mathematical
approach to noise and uncertain properties of nonlinear vibrations
arising in physics and engineering.