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Using functions in some function classes and a generalized Riccati technique, we establish Kamenev-type oscillation criteria for second-order dynamic equations with damping on time scales of the form (r(t)(xΔ(t))γ)Δ+p(t)(xΔ(t)γ)+f(t,x(g(t)))=0. Two examples are included to show the significance of the results.