The interaction of dark energy in the LRS Bianchi type-$I$ line element is explored on the background of $f(R,T)$ gravity, where $R$ and $T$ denotes the Ricci scalar together with the trace of energy momentum tensor of matter respectively. Here modified field equations are calculated using $f(R,T)=f_1 (R)+f_2 (T)$ together with inhomogeneous equation of state $(EoS)$, $p=\omega \rho -\Lambda (t)$, where $\omega$ is constant. The solutions of modified Einstein field equations (EFE) obtained are solved by taking a periodic time varying deceleration parameter (DP). Our model shows periodic nature with Big-Bang prevailing at time $t=0$. An investigation is done on the energy conditions and found that the conditions of null energy and strong energy are found to be violated. We analyse the geometrical and physical behaviours of these models.