  We show that the equivalent linearization technique, when used properly,
enables us to calculate frequency corrections of weakly nonlinear oscillators
beyond the first order in nonlinearity. We illustrate the method by applying it
to the conservative anharmonic oscillators and the nonconservative van der Pol
oscillator that are respectively paradigmatic systems for modeling center-type
oscillatory states and limit cycle type oscillatory states. The choice of these
systems is also prompted by the fact that first order frequency corrections may
vanish for both these types of oscillators, thereby rendering the calculation
of the higher order corrections rather important. The method presented herein
is very general in nature and, hence, in principle applicable to any arbitrary
periodic oscillator.
