A minimal model for oscillating between quiescent and growth/proliferation states, dependent on the availability of a central metabolic resource, is presented. From the yeast metabolic cycles, metabolic oscillations in oxygen consumption are represented as transitions between quiescent and growth states. We consider metabolic resource availability, growth rates, and switching rates (between states) to model a relaxation oscillator explaining transitions between these states. This frustrated bistability model reveals a required communication between the metabolic resource that determines oscillations and the quiescent and growth state cells. Cells in each state reflect memory, or hysteresis of their current state, and “push-pull” cells from the other state. Finally, a parsimonious argument is made for a specific central metabolite as the controller of switching between quiescence and growth states. We discuss how an oscillator built around the availability of such a metabolic resource is sufficient to generally regulate oscillations between growth and quiescence through committed transitions.