A new analytical technique to find periodic solutions of non-linear systems

Based on the classical harmonic balance method a new technique is presented to determine higher approximate periodic solutions of the non-linear differential equations. The new method is systematic and simple. The solution covers the general initial value problem (i.e., for [x(0)=a0,x˙(0)=b0]) while the existing solution is determined for a particular case, especially for [x(0)=a0,x˙(0)=0]. The solution is easily transformed to perturbation solution. The method is used in various non-linear problems possessing second and more than second derivatives.