In general, a physical system has invariant quantities which are very often related to its symmetry and to the invariance of the equation that describe it. A detailed study of the invariance property of the differential equation will be helpful in understanding this relation.
The work is concerned with a preliminary investigation of the Lie-group which leaves invariant the Newtonian and Lagrangian equation of motion for a one-dimensional harmonic oscillator. A brief review of Ehrenfest\u27s adiabatic principle and the later treatments on exact and adiabatic invariants will be presented
