Lie group Theory is applied to differential equations occurring as mathematical models [4]. This paper seeks to obtain a generator T for a harmonic fourth order non-linear ordinary differential equation using the Lie Symmetry group invariant Method. This method makes use of infinitesimal transformations. The Generator T of infinitesimal transformation is then used to obtain the general solution to our harmonic differential equation. The solution to our differential equation is handy in the field of mechanics.