## 2020-Zammit, Corey, Nirantha Balagopal, Zijun Li, Shenghao Xia, and Qisong Xiao - DynamicsOfElasticPendulum - Report

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Zammit, Corey, Nirantha Balagopal, Zijun Li, Shenghao Xia, and Qisong Xiao. THE DYNAMICS OF THE ELASTIC PENDULUM

The system of the elastic pendulum consists of a spring, connected to a pivot, suspending a mass. This spring can have many different properties among these are stiffness which can be considered a constant in some practical cases, so the spring has a linear reaction force when extended and compressed. Typically a spring that one would find in real-life applications is either an extension spring or a compression spring (and this will be discussed in greater detail in section 5) however for simplified models and preliminary research we find it practical to consider the case where this spring behaves in a Hookian manor in both extension and compression. This assumption, however, does beg this question among others: Does the spring bend as shown in Figure 1 when compressed ever, and how would this effect the behavior of the system? One way to answer this question is to acknowledge that assumptions such as the ones that follow need to be made to analyze this system, and in any case, behaviors such as these are not easy to analyze and would involve making many more assumptions that could be equally unsatisfying. We will be considering two regimes of this system in our preliminary research with the same assumptions and will pose questions for further research with suggestions for different assumptions.

**Keywords:** spring mass, pendulum, elastic, Hooke's Law

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