UNIVERSITY OF WEST ATTICA
SCHOOL OF ENGINEERING
DEPARTMENT OF COMPUTER ENGINEERING AND INFORMATICS

University of West Attica · Department of Computer Engineering and Informatics

---

Physics

Errors

Vasileios Evangelos Athanasiou
Student ID: 19390005

GitHub · LinkedIn

---

Supervision

Supervisor: Dimitrios Nikolopoulos, Professor

UNIWA Profile · LinkedIn

---

Athens, December 2019

---

---

README

Errors

This repository summarizes the physics project completed by Vasileios Evangelos Athanasiou for the University of West Attica. The project focuses on statistical error analysis, significant figures, and the least squares method applied to physical measurements.

---

Table of Contents

Section	Folder/File	Description
1	docs/	Documentation related to error analysis
1.1	docs/Errors.pdf	Error analysis document (English)
1.2	docs/Σφάλματα.pdf	Error analysis document (Greek)
2	tables/	Tables and datasets used in analysis
2.1	tables/Tables.xlsx	Error-related tables in spreadsheet format
2.2	tables/Πίνακες.pdf	Error-related tables in PDF format
3	README.md	Repository overview and usage instructions

---

1. Project Objectives

1.1 Significant Figures and Rounding

The project begins by identifying significant figures and performing rounding operations.

• Identification: Determining the number of significant figures (e.g., 976.45 → 5 significant figures).
• Rounding: Converting values to a defined number of significant figures (e.g., 8.314 → 8.3).

---

2. Statistical Analysis of Measurements

Experimental datasets are analyzed to compute statistical properties of measurements.

• Mean Value Calculation

$$ \bar{x} = \frac{1}{n}\sum x_i $$

• Standard Deviation of the Mean

$$ \sigma(\bar{x}) = \sqrt{\frac{\sum(\Delta x_i)^2}{n(n-1)}} $$

• Result Formatting

Final measurements are expressed with uncertainties, e.g.:

$$ (56.7 \pm 0.1),\text{cm} $$

---

3. Area Calculation and Error Propagation

The area of a rectangle is computed from measured dimensions with uncertainty propagation.

• Area Calculation

$$ \bar{A} = \bar{x} \times \bar{y} $$

• Error Propagation

Total uncertainty is derived from uncertainties of both dimensions.

---

4. Least Squares Method (Linear Regression)

The least squares method is applied to experimental measurements to determine physical constants.

4.1 Pendulum Motion

Analyzes the relation between oscillation period (T_i) and pendulum length (x_i) to determine:

• Gravity acceleration (g)
• Experimental constant (a)

4.2 Mass–Spring System

Uses oscillation periods (T_i) for varying masses (m_i) to compute:

• Spring constant (D)
• Effective mass of the spring (m_{ελ})

---

5. Summary of Calculated Constants

Based on experimental data:

• Gravity acceleration (g): 0.92145 cm²/s
• Spring Constant (D): 0.40807 N/m
• Calculated Area (A): 980.2 cm² ± 1.0%

---

6. Conclusion

The project demonstrates practical application of statistical methods, uncertainty analysis, and regression techniques in physics experiments, reinforcing foundational measurement and analysis skills.