This repository contains the final project for the course Quantification of Uncertainties in Physical Systems, conducted in June 2025.
The objective is to model a damped simple pendulum and quantify the effects of uncertainty in its length through a probabilistic framework and Monte Carlo simulation.
A simple damped pendulum is analyzed, considering uncertainty in its length L, modeled as a Gamma-distributed random variable. The angular response θ(t) is obtained via numerical integration of the linearized equation of motion, and statistical quantities of interest are computed from the ensemble of trajectories.
- Analytical modeling of a damped pendulum
- Small-angle approximation and linearization
- Uncertainty modeling using Gamma distributions
- Monte Carlo simulation (MC)
- Propagation of uncertainty in dynamic systems
- Statistical post-processing (mean, std, confidence intervals)
- Histogram and kernel density estimation (KDE)
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MATLAB
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Toolboxes:
- Statistics and Machine Learning
- ODE Suite
- MATLAB Base
This project was developed as the final assignment for the short course:
Quantification of Uncertainties in Physical Systems
Prof. Dr. Americo Barbosa da Cunha Junior
Institution: São Paulo State University (UNESP), School of Engineering, Ilha Solteira
The full technical report (in LaTeX) is available in the /Code and Report folder and will be submitted alongside this repository as part of the course evaluation.