Origami-inspired structures exhibit unique mechanical properties, making them promising candidates for deployable systems and programmable metamaterials. Their complex, repetitive geometries often lead to a large number of degrees of freedom, making conventional finite element (FE) simulations computa- tionally expensive. The bar-and-hinge framework offers an efficient modeling alternative by substituting origami panels with truss elements along the edges and using rotational springs to model folding and panel-bending. However, foundational works on this framework [1] have primarily focused on linear or nonlinear statics [2, 3]. Fundamental studies in the small-deformation linear regime [4] have qual- itatively explored dynamic behavior and bandgaps, but lacked quantitative validation with calibrated FE simulations or experiments. Bar-and-hinge-based investigations into large-deformation deployment dynamics as well as some experimental studies on origami dynamics have not been quantitatively com- pared with FE simulations. In summary, we observe a lack of rigorous studies informing the choice of bar-and-hinge parameters for simulating the structural dynamics of origami. This work addresses that gap by improving the bar-and-hinge model parameters for structural dynamics of origami, specifically for small-deformation modal analysis. We identify a range of low-frequency dynamic modes governed by folding and panel-bending, in which the bar-and-hinge framework can accurately capture dynamic be- havior. Bar-and-hinge parameters like lumped masses and rotational spring stiffnesses are derived using conservation laws and finite element tests, respectively. Using the proposed scheme, natural frequencies could be predicted with less than 10% maximum error across the range of modes, making it over three times more accurate than existing models. In majority of the cases, errors were below 5%, demonstrating that with proper calibration, bar-and-hinge models can be reliably used for efficient modal analysis of origami.