Summary: This paper is concerned with the asymptotic behavior of solutions of second order nonlinear dynamic equation \[ (r(t) x^\Delta(t))^\Delta+ p(t) \phi_\gamma(x(t))= 0, \] on an above-unbounded time scale \(\mathbb{T}\) where \(\gamma\) is a positive constant and where, in addition, \(r\) and \(p\) are real-valued, rd-continuous functions on \(\mathbb{T}\) with no explicit sign assumptions on \(p\). Our results are established for a time scale \(\mathbb{T}\) without assuming certain restrictive conditions on \(\mathbb{T}\). Several examples illustrating our results will be given.