This project introduces the concept of an inverse problem (or parameter estimation), in the context of the simple linearized pendulum ordinary differential equation. The theme of the project is that one often has a physical model for a system but in which the model contains unknown parameters or functions. The goal is to use the model along with data collected by observing the actual physical system to estimate the unknown parameter(s). Of particular interest are the questions of ``uniqueness'' (does the data contain the information needed to determine the parameter?), ``stability'' (do small errors in the data result in small errors in the parameter estimates?), and ``reconstruction'' (how can we constructively or explicitly obtain an estimate of the parameter from the data?) The project includes data collection and analysis in class.
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