Parameters Approach Applied on Nonlinear Oscillators

We applied an approach to obtain the natural frequency of the generalized Duffing oscillator <($)double over dot> + u + alpha(3)u(3) + alpha(5)u(5) + alpha(7)u(7) + ... + alpha(n)u(n) = 0 and a nonlinear oscillator with a restoring force which is the function of a noninteger power exponent of deflection <($)double over dot> + alpha u vertical bar u vertical bar(n-1) = 0. This approach is based on involved parameters, initial conditions, and collocation points. For any arbitrary power of n, the approximate frequency analysis is carried out between the natural frequency and amplitude. The solution procedure is simple, and the results obtained are valid for the whole solution domain.