Engineering Dynamics: Error Analysis in
Experimental Studies
Engineering Dynamics
Year 1
BEng Mechanical Engineering
Engineering Dynamics E1
1
,Abstract
The purpose of this study is to explain laboratory-generated experimental data errors. The
origins of inaccuracies during the experimental setting of measuring a mass' moment of
inertia were highlighted using a Trifilar suspension experiment. The setting involved timing
20 cycles, measuring the supporting swing's measurement length, and calculating the
aggregate mass of the plates. Learning how to calculate the overall uncertainty in the
measured value of the moment of inertia after adjusting for errors made during each stage of
the experiment.
The findings demonstrated that human error can significantly contribute to the uncertainty
of measured data, including errors in measuring oscillation duration, plate radius, and string
length.
The experiment emphasised error analysis's fundamental ideas and illustrated how it may be
used in actual laboratory work. A suggestion was made to increase the measured data's level
of uncertainty.
2
, Table of Contents
Abstract ................................................................................................................................................... 2
1.0 Introduction ................................................................................................................................ 5
1.1 Aims and Objectives ................................................................................................................ 5
2.0 Theory ......................................................................................................................................... 6
2.1 Moment of inertia ................................................................................................................... 6
2.2 The dynamics of the Trifilar suspension ................................................................................. 6
2.3 Principles of error analysis ...................................................................................................... 7
2.4 Error Analysis for the Trifilar suspension ................................................................................ 8
3.0 Apparatus .................................................................................................................................. 10
3.1 Weighting Scale..................................................................................................................... 10
3.2 Stopwatch ............................................................................................................................. 10
3.3 Tape measure........................................................................................................................ 10
3.4 Magnetic Spirit Level............................................................................................................. 10
3.5 Plate ...................................................................................................................................... 10
3.6 String ..................................................................................................................................... 10
3.7 Object .................................................................................................................................... 10
3.8 Trifilar suspension ................................................................................................................. 10
4.0 Method ..................................................................................................................................... 11
5.0 Result ........................................................................................................................................ 12
5.1 Time of Oscillating the Mass of Plate only ............................................................................ 12
5.2 Time of Oscillating the Combined Mass of Plate and Object: .............................................. 12
5.3 Uncertainties in measuring (δL), (δR), (δM) ............................................................................ 13
5.4 Calculating Moment of Inertia .............................................................................................. 13
5.4.1 Plate Mass Only .............................................................................................................................. 13
5.4.2 Combined Mass ................................................................................................................................... 13
5.5 Relative Uncertainties ........................................................................................................... 13
5.5.1 Plate Only ........................................................................................................................................ 13
5.5.2 Combined Masses: .......................................................................................................................... 14
5.6 Relative Uncertainties for IP & IC ........................................................................................... 14
5.6.1 Plate Only ........................................................................................................................................ 14
5.6.2 Combined Masses ........................................................................................................................... 15
5.7 Uncertainties for Measuring 𝛿𝐼𝑃 & 𝛿𝐼𝐶 .............................................................................. 15
5.7.1 Plate Only ........................................................................................................................................ 15
5.7.2 Combined Masses ........................................................................................................................... 15
5.8 Uncertainty for measuring the moment of Inertia of the object ......................................... 15
3
, 5.9 Percentage Error Band .......................................................................................................... 16
6.0 Discussion.................................................................................................................................. 17
6.1 Question 1 ............................................................................................................................. 17
6.2 Question 2 ............................................................................................................................. 17
6.3 Question 3 ............................................................................................................................. 18
6.3.1 Plate Only ........................................................................................................................................ 18
6.3.2 Combined Mass .............................................................................................................................. 18
6.4 Question 4 ............................................................................................................................. 18
6.5 Question 5 ............................................................................................................................. 19
6.6 Question 6 ............................................................................................................................. 19
7.0 Conclusion ................................................................................................................................. 21
Bibliography .......................................................................................................................................... 22
Appendix A – Figures ............................................................................................................................ 23
Appendix B – Tables .............................................................................................................................. 26
Appendix C – Graphs ............................................................................................................................. 27
List of Figures (Appendix A)
Figure 1: Trifilar Suspension .................................................................................................................. 23
Figure 2: Weighing Scale ....................................................................................................................... 23
Figure 3: Stopwatch .............................................................................................................................. 24
Figure 4: Tape Measure ........................................................................................................................ 24
Figure 5: Magnetic Spirit Level.............................................................................................................. 24
Figure 6: Plate ....................................................................................................................................... 25
Figure 7: Object placed on plate ........................................................................................................... 25
Figure 8: Trifilar Suspension. ................................................................................................................. 25
List of Tables (Appendix B)
Table 1: Results Processing Presentation ............................................................................................. 26
List of Graphs (Appendix C)
4
, 1.0 Introduction
The likelihood of errors in experimental investigations conducted in engineering and science
is extremely high. So that the experiment cannot be misinterpreted or called into question, it
is crucial for the credibility of the experimental activity to understand the origins of errors and
how to evaluate them. Thus, learning error analysis is essential for every scientist and
engineer. Understanding and mastering the crucial ability of understanding and quantifying
errors and uncertainties in the experimental data.
In this laboratory experiment, the moment of inertia of a mass (also known as the second
moment of mass) is measured using a Trifilar suspension apparatus (APPENDIX A, figure 1).
1.1 Aims and Objectives
The purpose of this laboratory experiment is to better understand how to analyse errors in
experimental activity. Learn how to calculate the uncertainty in experimental data and the
sources of errors. The goal of the experimental effort is to use an error analysis understanding
in a Trifilar suspension experiment to determine a mass' moment of inertia. The experiment
illustrated the relationship between errors in an experimental setting (in each phase of the
experiment) and the uncertainties of each step in order to calculate the "total" uncertainty in
the conclusion, which is the mass's moment of inertia. [1]
5
Experimental Studies
Engineering Dynamics
Year 1
BEng Mechanical Engineering
Engineering Dynamics E1
1
,Abstract
The purpose of this study is to explain laboratory-generated experimental data errors. The
origins of inaccuracies during the experimental setting of measuring a mass' moment of
inertia were highlighted using a Trifilar suspension experiment. The setting involved timing
20 cycles, measuring the supporting swing's measurement length, and calculating the
aggregate mass of the plates. Learning how to calculate the overall uncertainty in the
measured value of the moment of inertia after adjusting for errors made during each stage of
the experiment.
The findings demonstrated that human error can significantly contribute to the uncertainty
of measured data, including errors in measuring oscillation duration, plate radius, and string
length.
The experiment emphasised error analysis's fundamental ideas and illustrated how it may be
used in actual laboratory work. A suggestion was made to increase the measured data's level
of uncertainty.
2
, Table of Contents
Abstract ................................................................................................................................................... 2
1.0 Introduction ................................................................................................................................ 5
1.1 Aims and Objectives ................................................................................................................ 5
2.0 Theory ......................................................................................................................................... 6
2.1 Moment of inertia ................................................................................................................... 6
2.2 The dynamics of the Trifilar suspension ................................................................................. 6
2.3 Principles of error analysis ...................................................................................................... 7
2.4 Error Analysis for the Trifilar suspension ................................................................................ 8
3.0 Apparatus .................................................................................................................................. 10
3.1 Weighting Scale..................................................................................................................... 10
3.2 Stopwatch ............................................................................................................................. 10
3.3 Tape measure........................................................................................................................ 10
3.4 Magnetic Spirit Level............................................................................................................. 10
3.5 Plate ...................................................................................................................................... 10
3.6 String ..................................................................................................................................... 10
3.7 Object .................................................................................................................................... 10
3.8 Trifilar suspension ................................................................................................................. 10
4.0 Method ..................................................................................................................................... 11
5.0 Result ........................................................................................................................................ 12
5.1 Time of Oscillating the Mass of Plate only ............................................................................ 12
5.2 Time of Oscillating the Combined Mass of Plate and Object: .............................................. 12
5.3 Uncertainties in measuring (δL), (δR), (δM) ............................................................................ 13
5.4 Calculating Moment of Inertia .............................................................................................. 13
5.4.1 Plate Mass Only .............................................................................................................................. 13
5.4.2 Combined Mass ................................................................................................................................... 13
5.5 Relative Uncertainties ........................................................................................................... 13
5.5.1 Plate Only ........................................................................................................................................ 13
5.5.2 Combined Masses: .......................................................................................................................... 14
5.6 Relative Uncertainties for IP & IC ........................................................................................... 14
5.6.1 Plate Only ........................................................................................................................................ 14
5.6.2 Combined Masses ........................................................................................................................... 15
5.7 Uncertainties for Measuring 𝛿𝐼𝑃 & 𝛿𝐼𝐶 .............................................................................. 15
5.7.1 Plate Only ........................................................................................................................................ 15
5.7.2 Combined Masses ........................................................................................................................... 15
5.8 Uncertainty for measuring the moment of Inertia of the object ......................................... 15
3
, 5.9 Percentage Error Band .......................................................................................................... 16
6.0 Discussion.................................................................................................................................. 17
6.1 Question 1 ............................................................................................................................. 17
6.2 Question 2 ............................................................................................................................. 17
6.3 Question 3 ............................................................................................................................. 18
6.3.1 Plate Only ........................................................................................................................................ 18
6.3.2 Combined Mass .............................................................................................................................. 18
6.4 Question 4 ............................................................................................................................. 18
6.5 Question 5 ............................................................................................................................. 19
6.6 Question 6 ............................................................................................................................. 19
7.0 Conclusion ................................................................................................................................. 21
Bibliography .......................................................................................................................................... 22
Appendix A – Figures ............................................................................................................................ 23
Appendix B – Tables .............................................................................................................................. 26
Appendix C – Graphs ............................................................................................................................. 27
List of Figures (Appendix A)
Figure 1: Trifilar Suspension .................................................................................................................. 23
Figure 2: Weighing Scale ....................................................................................................................... 23
Figure 3: Stopwatch .............................................................................................................................. 24
Figure 4: Tape Measure ........................................................................................................................ 24
Figure 5: Magnetic Spirit Level.............................................................................................................. 24
Figure 6: Plate ....................................................................................................................................... 25
Figure 7: Object placed on plate ........................................................................................................... 25
Figure 8: Trifilar Suspension. ................................................................................................................. 25
List of Tables (Appendix B)
Table 1: Results Processing Presentation ............................................................................................. 26
List of Graphs (Appendix C)
4
, 1.0 Introduction
The likelihood of errors in experimental investigations conducted in engineering and science
is extremely high. So that the experiment cannot be misinterpreted or called into question, it
is crucial for the credibility of the experimental activity to understand the origins of errors and
how to evaluate them. Thus, learning error analysis is essential for every scientist and
engineer. Understanding and mastering the crucial ability of understanding and quantifying
errors and uncertainties in the experimental data.
In this laboratory experiment, the moment of inertia of a mass (also known as the second
moment of mass) is measured using a Trifilar suspension apparatus (APPENDIX A, figure 1).
1.1 Aims and Objectives
The purpose of this laboratory experiment is to better understand how to analyse errors in
experimental activity. Learn how to calculate the uncertainty in experimental data and the
sources of errors. The goal of the experimental effort is to use an error analysis understanding
in a Trifilar suspension experiment to determine a mass' moment of inertia. The experiment
illustrated the relationship between errors in an experimental setting (in each phase of the
experiment) and the uncertainties of each step in order to calculate the "total" uncertainty in
the conclusion, which is the mass's moment of inertia. [1]
5
