We study entanglement dynamics in a dispersive optomechanical system consisting of two optical modes and a mechanical oscillator inside an optical cavity.The two optical modes interact with the mechanical oscillator, but not Course a pied - Accessoires - Nutrition - Barres directly with each other.The appearance of optical entanglement witnesses nonclassicality of the oscillator.We study the dependence of the entanglement dynamics on the optomechanical coupling, the mean photon number in the cavity, and the Alkaline Battery oscillator temperature.An experimental realization with ultracold atomic ensembles is proposed.