ACADEMIC PAPERS
MATHEMATICS/ENGINEERING
2020
EXPLORING CHAOS IN A DOUBLE PENDULUM
On reading "17 Equations that changed the world" by Ian Stewart and "Chaos" by James Gleick, I was inspired to write a paper exploring the wonderful intricacies of Chaos Theory. I investigated this through a deceptively simple model of a double pendulum. I began by deriving the equations for the for the double pendulum using the Lagrangian (TV) and then used the Euler Lagrange Equations to obtain 4 differential equations. I also modified my equations to factor in a damping force using the Rayleigh Dissipation Function.
I inputed my derived equations into Python to create a program that could follow the motion of the double pendulum. Finally I compared my computer simulation to an experimental model I had built, to see if I had managed to predict even a fraction of the time that the pendulum was moving for.
What made the project very fascinating was the inherent nature of deterministic chaos that made any prediction beyond a few seconds almost impossible without measurement tools with extremely high accuracy.
Nonetheless, the findings of my exploration and the handson experience of building my own double pendulum and writing my own code was very fruitful.
ANALYSIS OF THE BIG O NOTATION AND ITS EVALUATION OF THE TIME COMPLEXITIES OF SORTING ALGORITHMS
Having been interested in computers from a young age, I always wanted to explore how they functioned, and how they were so fast. Recently I watched a video that looked at how a single algorithm ruined an entire project because it simply wasn't efficient.
Thus I was inspired to explore the efficiency of a bedrock of modern computers  Sorting Algorithms.
To do this I explored Sorting Theory and several factors used to measure the efficiency of algorithms. In my Essay I focused on the "Big O Notations"  a form of asymptotic notation that gives programmers a general idea of the efficiency of algorithms as it measures their time complexity.
I explored the following algorithms:

Permutation Sort

Bubble Sort

Quick Sort

Merge Sort

Counting sort
The analysis of the data I obtained from running trials for the "time to sort" yielded some surprising results.
PHYSICS
2020
WINE GLASS HARMONICS AND LIQUID DENSITY
Stuck in the house during the lockdown, I did not have access to a laboratory to make precise measurements. Instead, I used my interest in music and my passion for frugality, to convert my room into a makeshift lab.
The obvious constraints that my homelab with kitchen tools for measurement made conducting experiments more challenging, yet I did not want to explore something that had been widely researched before. Rather than looking at how the height of water in a wine glass impacts its resonant frequency, I explored how the density of liquid in the wine glass impacts it's resonant frequency.
I used the AP French Equation:
As a theoretical prediction of the frequency.
I manipulated densities by adding different salt concentrations to the liquid (water) in my wine glass. Through my investigation, I confirmed a direct linear relationship between the density of the liquid and the reciprocal of the square of the measured frequency.