This is the first group project I worked on in Mathematical Modeling Case Studies. We were given two weeks to complete this project.
The motivation of this project was to first model the amplitude of a damped pendulum at varied arm lengths using exponential and power fits. After producing our fits, a second objective was to determine which of the fits, power law or exponential, would be a more accurate fit to the envelope of our data. We decided to fit power law and exponential curves to our data because the data from our underdamped pendulum appeared to be a sinusoid enveloped by a decaying exponential. For collecting data, we used a rotational motion sensor and computer software from the Pasco data studio acquistion system. Next we used Matlab code to fit power law and exponential curves to our data. We then created plots of the residuals from both fits and compared the residual patterns and relative errors to determine the best model for the damped pendulum. From the results of our project we have decided that the exponential fit holds as a strong model for a damped pendulum, regardless of varied arm lengths.