Here we closely examine the change of sign in the potential energy of the system with respect to all disturbances

Etudes

Here we closely examine the change of sign in the potential energy of the system with respect to all disturbances. If we observe a negative sign then the potential energy characterizing the system decreases for some disturbance and the kinetic energy is available for motion to depart away from the equilibrium state and the system becomes unstable. This method gives the condition of stability but not the dispersion relation, by which growth rate of instability can be obtained. Therefore, energy methods quite effectively used for conservative systems in which there is no dissipation of the energy and it is used to obtain the natural frequency of some simple systems.