Conventional crank-based engines are limited by mechanical, thermal, and combustion inefficiencies. The free piston of a linear engine generator reduces frictional losses by avoiding the rotational motion and crankshaft linkages. Instead, electrical power is generated by the oscillation of a translator through a linear stator. Because the free piston is not geometrically constrained, dead center positions are not specifically known. This results in a struggle against adverse events like misfire, stall, over-fueling, or rapid load changes. It is the belief that incorporating springs will have the dual benefit of increasing frequency and providing a restoring force to aid in greater cycle to cycle stability. For dual free piston linear engines the addition of springs has not been fully explored, despite growing interest and literature. This investigation reviews the current modeling literature and advances the fundamental understanding of the free piston linear engine with springs by developing an idealized, nondimensional model. The model combines the dynamics of a damped, spring mass system with in-cylinder thermodynamic expressions. Simplifying assumptions are made to represent perfect springs, ideal gases, instantaneous heat addition and rejection, and an average friction force for work output dependent on stroke length. The model is executed for selected cases to represent the fundamental nature of the system. The model is explored both in and out of the context of the Otto cycle to demonstrate natural and forced stability over multiple operation cycles. Then, it is shown that system frequency and relative indicated mean effective pressure can be raised by increasing the baseline cylinder pressure, the bore diameter, or the amount of heat added through combustion relative to the stiffness of the spring. Lastly, the benefits of lower temperature operation are reinforced through parameterization of the specific heat ratio.