MECH 375 LAB 4 Experiment 4: Characteristics Of A Multi
Degree-Of-Freedom System FALL 2025-2026 Concordia
University
Experiment 4:
Characteristics Of A Multi Degree-Of-Freedom System
Submitted by
Lab Section EI – X
Summer 2025
Professor Subhash Rakheja
Concordia University
Montreal, QC, Canada
1
,Table of Contents
Table of Contents ..................................................................................... 2
Objective ............................................................................................ 4
Introduction ......................................................................................... 4
Procedure ........................................................................................... 6
Results ............................................................................................... 8
Experiment 4.1 ................................................................................... 8
Experiment 4.2 ................................................................................. 12
Sample Calculations............................................................................ 16
Equations ..................................................................................... 16
Experiment 4.1 ............................................................................... 16
Experiment 4.2 ............................................................................... 17
Discussion ......................................................................................... 18
Experiment 4.1 ................................................................................. 18
Experiment 4.2 ................................................................................. 18
Conclusion......................................................................................... 18
References ........................................................................................ 20
2
, List of Figures
Figure 1: Multi degree-of-freedom (MDOF) torsional system excited by external force [1] ...4
Figure 2: Semi-definite MDOF torsional system [1] .............................................. 5
Figure 3: Mode shape at fundamental natural frequency for semi-definite MDOF system ... 6
Figure 4: Lab 4 part 1 experimental mode shapes ................................................ 9
Figure 5: Lab 4 part 1 Matlab code ............................................................... 10
Figure 6: Lab 4 part 1 Matlab theoretical mode shapes ........................................ 11
Figure 7: Lab 4 part 2 Matlab code ............................................................... 14
Figure 8: Lab 4 part 2 Matlab theoretical mode shapes ........................................ 15
List of Tables
Table 1: Lab 4 part 1 experimental results......................................................... 8
Table 2: Lab 4 part 2 experimental results....................................................... 12
Table 3: Lab 4 part 2 experimental mode shapes ............................................... 13
3
Degree-Of-Freedom System FALL 2025-2026 Concordia
University
Experiment 4:
Characteristics Of A Multi Degree-Of-Freedom System
Submitted by
Lab Section EI – X
Summer 2025
Professor Subhash Rakheja
Concordia University
Montreal, QC, Canada
1
,Table of Contents
Table of Contents ..................................................................................... 2
Objective ............................................................................................ 4
Introduction ......................................................................................... 4
Procedure ........................................................................................... 6
Results ............................................................................................... 8
Experiment 4.1 ................................................................................... 8
Experiment 4.2 ................................................................................. 12
Sample Calculations............................................................................ 16
Equations ..................................................................................... 16
Experiment 4.1 ............................................................................... 16
Experiment 4.2 ............................................................................... 17
Discussion ......................................................................................... 18
Experiment 4.1 ................................................................................. 18
Experiment 4.2 ................................................................................. 18
Conclusion......................................................................................... 18
References ........................................................................................ 20
2
, List of Figures
Figure 1: Multi degree-of-freedom (MDOF) torsional system excited by external force [1] ...4
Figure 2: Semi-definite MDOF torsional system [1] .............................................. 5
Figure 3: Mode shape at fundamental natural frequency for semi-definite MDOF system ... 6
Figure 4: Lab 4 part 1 experimental mode shapes ................................................ 9
Figure 5: Lab 4 part 1 Matlab code ............................................................... 10
Figure 6: Lab 4 part 1 Matlab theoretical mode shapes ........................................ 11
Figure 7: Lab 4 part 2 Matlab code ............................................................... 14
Figure 8: Lab 4 part 2 Matlab theoretical mode shapes ........................................ 15
List of Tables
Table 1: Lab 4 part 1 experimental results......................................................... 8
Table 2: Lab 4 part 2 experimental results....................................................... 12
Table 3: Lab 4 part 2 experimental mode shapes ............................................... 13
3
