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In this report we have presented a brief review of the glass transition and one means of characterizing glassy materials: linear and nonlinear thermodynamic oscillatory experiments to extract the dynamic heat capacity. We have applied these methods to the east model (a variation of the Ising model for glass forming systems) and a simple polymeric system via molecular dynamics simulation, and our results match what is seen in experiment. For the east model, since the dynamics are so simple, a mathematical model is developed that matches the simulated dynamics. For the polymeric system, since the system is a simulation, we can instantaneously 'quench' the system - removing all vibrational energy - to separate the vibrational dynamics from dynamics associated with particle rearrangements. This shows that the long-time glassy dynamics are due entirely to the particle rearrangements, i.e. basin jumping on the potential energy landscape. Finally, we present an extension of linear dynamic heat capacity to the nonlinear regime

Dynamic heat capacity of the east model and of a bead-spring polymer model.