Here we describe a problem class with combined architecture, plant, and control design for dynamic engineering systems. The design problem class is characterized by architectures comprised of linear physical elements and nested co-design optimization problems employing linear-quadratic dynamic optimization. The select problem class leverages a number of existing theory and tools and is particularly effective due to the symbiosis between labeled graph representations of architectures, dynamic models constructed from linear physical elements, linear-quadratic dynamic optimization, and the nested co-design solution strategy. A vehicle suspension case study is investigated and a specifically constructed architecture, plant, and control design problem is described. The result was the automated generation and co-design problem evaluation of 4374 unique suspension architectures. The results demonstrate that changes to the vehicle suspension architecture can result in improved performance, but at the cost of increased mechanical complexity. Furthermore, the case study highlights a number of challenges associated with finding solutions to the considered class of design problems. One such challenge is the requirement to use simplified design problem elements/models; thus, the goal of these early-stage studies are to identify new architectures that are worth investigating more deeply. The results of higher-fidelity studies on a subset of high-performance architectures can then be used to select a final system architecture. In many aspects, the described problem class is the simplest case applicable to graph-representable, dynamic engineering systems.