Overview

This unit of study aims to introduce students to the underlying fundamentals of mechanical vibrations, and the analysis of data that is obtained from the measurement of these systems. Students will be able to recognize the fundamental components required for vibration to occur, and produce mathematical models of vibrating systems. Students will be able to analyse the dynamics of these systems using Fourier analysis techniques, as well as emerging techniques in data-driven decomposition. The presentation of the material focuses on the practical application and analysis of vibrations using examples and virtual experiments.

Requisites

Prerequisites
MTH10012 Calculus and Applications

AND
MTH10013 Linear Algebra and Applications
AND
Completion of 150 credit points

OR

For PDE:
MTH10007 Engineering Mathematics 2 
OR
MTH10003 Engineering Mathematics 2P 
AND
Completion of 150 credit points

Teaching periods
Location
Start and end dates
Last self-enrolment date
Census date
Last withdraw without fail date
Results released date
Semester 1
Location
Hawthorn
Start and end dates
02-March-2026
31-May-2026
Last self-enrolment date
15-March-2026
Census date
31-March-2026
Last withdraw without fail date
21-April-2026
Results released date
07-July-2026

Unit learning outcomes

Students who successfully complete this unit will be able to:
 

  1. Understand and implement the mathematical modelling of mechanically vibrating systems and analyze the solutions of these systems (K1, K2, K3, S1)
  2. Apply signal sampling and Nyquist theory to design acquisition systems (K2, K3, S1, S2, S3)
  3. Apply digital filters, time and frequency domain analysis techniques to signal processing (K2, K3, S1, S2, S3)
  4. Apply Fourier series and the Fast Fourier Transform to analysing sound and vibration signals (K2, K3, S1)
  5. Apply data-driven computation techniques and regression methods to decompose and interpret empirical data (K2, K3, K4, S1, S2)

Teaching methods

Hawthorn

Activity Type Hours per week Number of weeks Total (number of hours)

Online
Lecture

 2.00 12 weeks 24
On-Campus
Class		 2.00 3 weeks 6
On-Campus
Class		 2.00 9 weeks 18
On-Campus
Lecture		 1.00 12 weeks 12
Unspecified Activities 
Independent learning		 4.00 12 weeks 48
Unspecified Activities 
Assessment Preparation		 3.50 12 weeks 42
Total     150

Assessment

Type Task Weighting ULOs
Major Assignment Individual 40-60 % 1, 2, 3, 4, 5
Online Quizzes Individual 10-20 % 1, 2, 3, 4, 5
Test 2 Individual 10-20 % 2, 3, 4, 5
Mid-Semester Test Individual 10-20 % 1

Content

  • Fundamentals of free mechanical vibration in one degree of freedom
  • Forced or driven vibration in one degree of freedom
  • Free and forced vibration in multiple degrees of freedom
  • Vibration control and nonlinear vibration
  • Fourier series and Fourier transforms
  • Sampling, aliasing and filtering
  • Fourier analysis extensions to multiple dimensions
  • Data-driven decomposition in one dimension using Empirical Mode Decomposition
  • Data-driven decomposition in multiple dimensions using Proper Orthogonal Decomposition

GA 5 - Digital Literacies 1 - Information literacy

GA 6 - Digital Literacies 2 - Technical literacy

Study resources

Reading materials

A list of reading materials and/or required textbooks will be available in the Unit Outline on Canvas.