We consider the equilibrium perturbations for two stochastic systems: the $d$-dimensional generalized exclusion process and the one-dimensional chain of anharmonic oscillators. We add a perturbation of order $N^{-α}$ to the equilibrium profile and speed up the process by $N^{1+κ}$ for parameters $0<κ\leα$. Under some additional constraints on $κ$ and $α$, we show the perturbed quantities evolve according to the Burgers equation in the exclusion process, and to two decoupled Burgers equations in the anharmonic chain, both in the smooth regime.