This paper explores the oscillatory behavior of solutions to a class of second-order dynamic equations of the form \(\begin{aligned} \left( b(t)\left( {\mathcal {X}}^{\Delta }(t)\right) ^{\alpha _{1}}\right) ^{\Delta }= q(t) {\mathcal {X}}^{\alpha _{1}}(\delta (t)) \end{aligned}\) on a time scale \({\mathbb {T}}\) with \(\sup {{\mathbb {T}}}=\infty \) . By using two suitable sequences, we eliminate all possible non-oscillatory solutions to establish the desired results. To support our theoretical results, we provide entirely novel results for the particular case \(\begin{aligned} \Delta \left( b(t)\left( \Delta {\mathcal {X}}(t)\right) ^{\alpha _{1}}\right) = q(t) {\mathcal {X}}^{\alpha _{1}}(\delta (t)), \end{aligned}\) where \(\Delta {\mathcal {X}}(t)={\mathcal {X}}(t+1)-{\mathcal {X}}(t)\) , and demonstrate these results through three illustrative examples using Matlab.
