The author considers the second-order scalar dynamic equation
on a time scale , where , is assumed to be rd-continuously differentiable, is rd-continuous and the graininess is not identically zero on , for large . Using averaging techniques, criteria for the oscillatory behavior of are deduced, which extend earlier results by the author for difference equations in [J. Math. Anal. Appl., 142, No. 2, 468–487 (1989, Zbl 0686.39001)]. In particular, these criteria indicate how oscillation depends on the graininess of the time scale. Finally, two examples illustrate the obtained results.