We study entanglement dynamics in a dispersive optomechanical system consisting of two optical modes and a mechanical oscillator inside an optical cavity.The one eared bridles two optical modes interact with the mechanical oscillator, but not directly with each other.The appearance of optical entanglement witnesses nonclassicality of the oscillator.We study C-STRAIGHT SMOOTHING SHAMPOO the dependence of the entanglement dynamics on the optomechanical coupling, the mean photon number in the cavity, and the oscillator temperature.An experimental realization with ultracold atomic ensembles is proposed.